How to graph a line - PSAT Math

Card 0 of 42

Question

The equation represents a line. This line does NOT pass through which of the four quadrants?

Answer

Plug in for to find a point on the line:

Thus, is a point on the line.

Plug in for to find a second point on the line:

is another point on the line.

Now we know that the line passes through the points and .

A quick sketch of the two points reveals that the line passes through all but the third quadrant.

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Question

A line graphed on the coordinate plane below.

Give the equation of the line in slope intercept form.

Answer

The slope of the line is $\dpi{100} \small -2$ and the y-intercept is $\dpi{100} \small 4$ .

The equation of the line is $\dpi{100} \small y=-2x+4$ .

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Question

Give the equation of the curve.

Answer

This is the parent graph of $\dpi{100} \small x^{3}$ . Since the graph in question is negative, then we flip the quadrants in which it will approach infinity. So the graph of $\dpi{100} \small y=-x^{3}$ will start in quadrant 2 and end in 4.

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Question

What is the equation of the line in the graph above?

Answer

In order to find the equation of a line in slope-intercept form $\left( y = mx+b$ , where is the slope and is the y-intercept), one must know or otherwise figure out the slope of the line (its rate of change) and the point at which it intersects the y-axis. By looking at the graph, you can see that the line crosses the y-axis at . Therefore, .

Slope is the rate of change of a line, which can be calculated by figuring out the change in y divided by the change in x, using the formula

$m = \frac{\Delta y}{\Delta x} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ .

When looking at a graph, you can pick two points on a graph and substitute their x- and y-values into that equation. On this graph, it's easier to choose points like and . Plug them into the equation, and you get

$m = \frac{1+1}{1-0} = \frac{2}{1} = 2$

Plugging in those values for and in the equation, and you get

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Question

What are the x- and y- intercepts of the equation ?

Answer

Answer: (1/2,0) and (0,-2)

Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equation is in slope-intercept () form, meaning that the y-intercept, b, is actually given in the equation. b = -2, which means that our y-intercept is -2. The ordered pair for expressing this is (0,-2)

Finding the x-intercept: To find the x-intercept of the equation , we must find the point where the line of the equation crosses the x-axis. In other words, we must find the point on the line where y is equal to 0, as it is when crossing the x-axis. Therefore, substitute 0 into the equation and solve for x:

The x-interecept is therefore (1/2,0).

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Question

Which of the following could be the equation of the line shown in this graph?

Answer

The line in the diagram has a negative slope and a positive y-intercept. It has a negative slope because the line moves from the upper left to the lower right, and it has a positive y-intercept because the line intercepts the y-axis above zero.

The only answer choice with a negative slope and a positive y-intercept is

$y=-\frac{2}{3}x +1$

Compare your answer with the correct one above

Question

The equation represents a line. This line does NOT pass through which of the four quadrants?

Answer

Plug in for to find a point on the line:

Thus, is a point on the line.

Plug in for to find a second point on the line:

is another point on the line.

Now we know that the line passes through the points and .

A quick sketch of the two points reveals that the line passes through all but the third quadrant.

Compare your answer with the correct one above

Question

A line graphed on the coordinate plane below.

Give the equation of the line in slope intercept form.

Answer

The slope of the line is $\dpi{100} \small -2$ and the y-intercept is $\dpi{100} \small 4$ .

The equation of the line is $\dpi{100} \small y=-2x+4$ .

Compare your answer with the correct one above

Question

Give the equation of the curve.

Answer

This is the parent graph of $\dpi{100} \small x^{3}$ . Since the graph in question is negative, then we flip the quadrants in which it will approach infinity. So the graph of $\dpi{100} \small y=-x^{3}$ will start in quadrant 2 and end in 4.

Compare your answer with the correct one above

Question

What is the equation of the line in the graph above?

Answer

In order to find the equation of a line in slope-intercept form $\left( y = mx+b$ , where is the slope and is the y-intercept), one must know or otherwise figure out the slope of the line (its rate of change) and the point at which it intersects the y-axis. By looking at the graph, you can see that the line crosses the y-axis at . Therefore, .

Slope is the rate of change of a line, which can be calculated by figuring out the change in y divided by the change in x, using the formula

$m = \frac{\Delta y}{\Delta x} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ .

When looking at a graph, you can pick two points on a graph and substitute their x- and y-values into that equation. On this graph, it's easier to choose points like and . Plug them into the equation, and you get

$m = \frac{1+1}{1-0} = \frac{2}{1} = 2$

Plugging in those values for and in the equation, and you get

Compare your answer with the correct one above

Question

What are the x- and y- intercepts of the equation ?

Answer

Answer: (1/2,0) and (0,-2)

Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equation is in slope-intercept () form, meaning that the y-intercept, b, is actually given in the equation. b = -2, which means that our y-intercept is -2. The ordered pair for expressing this is (0,-2)

Finding the x-intercept: To find the x-intercept of the equation , we must find the point where the line of the equation crosses the x-axis. In other words, we must find the point on the line where y is equal to 0, as it is when crossing the x-axis. Therefore, substitute 0 into the equation and solve for x:

The x-interecept is therefore (1/2,0).

Compare your answer with the correct one above

Question

Which of the following could be the equation of the line shown in this graph?

Answer

The line in the diagram has a negative slope and a positive y-intercept. It has a negative slope because the line moves from the upper left to the lower right, and it has a positive y-intercept because the line intercepts the y-axis above zero.

The only answer choice with a negative slope and a positive y-intercept is

$y=-\frac{2}{3}x +1$

Compare your answer with the correct one above

Question

What are the x- and y- intercepts of the equation ?

Answer

Answer: (1/2,0) and (0,-2)

Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equation is in slope-intercept () form, meaning that the y-intercept, b, is actually given in the equation. b = -2, which means that our y-intercept is -2. The ordered pair for expressing this is (0,-2)

Finding the x-intercept: To find the x-intercept of the equation , we must find the point where the line of the equation crosses the x-axis. In other words, we must find the point on the line where y is equal to 0, as it is when crossing the x-axis. Therefore, substitute 0 into the equation and solve for x:

The x-interecept is therefore (1/2,0).

Compare your answer with the correct one above

Question

The equation represents a line. This line does NOT pass through which of the four quadrants?

Answer

Plug in for to find a point on the line:

Thus, is a point on the line.

Plug in for to find a second point on the line:

is another point on the line.

Now we know that the line passes through the points and .

A quick sketch of the two points reveals that the line passes through all but the third quadrant.

Compare your answer with the correct one above

Question

A line graphed on the coordinate plane below.

Give the equation of the line in slope intercept form.

Answer

The slope of the line is $\dpi{100} \small -2$ and the y-intercept is $\dpi{100} \small 4$ .

The equation of the line is $\dpi{100} \small y=-2x+4$ .

Compare your answer with the correct one above

Question

Give the equation of the curve.

Answer

This is the parent graph of $\dpi{100} \small x^{3}$ . Since the graph in question is negative, then we flip the quadrants in which it will approach infinity. So the graph of $\dpi{100} \small y=-x^{3}$ will start in quadrant 2 and end in 4.

Compare your answer with the correct one above

Question

What is the equation of the line in the graph above?

Answer

In order to find the equation of a line in slope-intercept form $\left( y = mx+b$ , where is the slope and is the y-intercept), one must know or otherwise figure out the slope of the line (its rate of change) and the point at which it intersects the y-axis. By looking at the graph, you can see that the line crosses the y-axis at . Therefore, .

Slope is the rate of change of a line, which can be calculated by figuring out the change in y divided by the change in x, using the formula

$m = \frac{\Delta y}{\Delta x} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ .

When looking at a graph, you can pick two points on a graph and substitute their x- and y-values into that equation. On this graph, it's easier to choose points like and . Plug them into the equation, and you get

$m = \frac{1+1}{1-0} = \frac{2}{1} = 2$

Plugging in those values for and in the equation, and you get

Compare your answer with the correct one above

Question

Which of the following could be the equation of the line shown in this graph?

Answer

The line in the diagram has a negative slope and a positive y-intercept. It has a negative slope because the line moves from the upper left to the lower right, and it has a positive y-intercept because the line intercepts the y-axis above zero.

The only answer choice with a negative slope and a positive y-intercept is

$y=-\frac{2}{3}x +1$

Compare your answer with the correct one above

Question

What are the x- and y- intercepts of the equation ?

Answer

Answer: (1/2,0) and (0,-2)

Finding the y-intercept: The y-intercept is the point at which the line crosses tye y-axis, meaning that x = 0 and the format of the ordered pair is (0,y) with y being the y-intercept. The equation is in slope-intercept () form, meaning that the y-intercept, b, is actually given in the equation. b = -2, which means that our y-intercept is -2. The ordered pair for expressing this is (0,-2)

Finding the x-intercept: To find the x-intercept of the equation , we must find the point where the line of the equation crosses the x-axis. In other words, we must find the point on the line where y is equal to 0, as it is when crossing the x-axis. Therefore, substitute 0 into the equation and solve for x:

The x-interecept is therefore (1/2,0).

Compare your answer with the correct one above

Question

The equation represents a line. This line does NOT pass through which of the four quadrants?

Answer

Plug in for to find a point on the line:

Thus, is a point on the line.

Plug in for to find a second point on the line:

is another point on the line.

Now we know that the line passes through the points and .

A quick sketch of the two points reveals that the line passes through all but the third quadrant.

Compare your answer with the correct one above

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