Functions and Lines

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Algebra › Functions and Lines

Questions 1 - 10
1

Find the slope of the line that passes through the following points:

and

Explanation

Use the following formula to find the slope of the line:

Remember that points are written in the following format:

For this line,

Subtracting a negative number is the same as adding a positive number.

Simplify.

2

If , solve for if .

Explanation

We are given an equation that is a function of x. Substitute the given fraction and replace it with the variable.

Simplify the right side.

The answer is:

3

Explanation

4

What's the slope of the line perpendicular to ?

Explanation

When finding the slope of a perpendicular line, we need to ensure we have form.

stands for slope.

Our is .

To find the perpendicular slope, we need to take the negative reciprocal of that value which is .

5

Find the slope of the line that passes through the following points:

and

Explanation

Use the following formula to find the slope of the line:

Remember that points are written in the following format:

For this line,

Subtracting a negative number is the same as adding a positive number.

Simplify.

6

Find the slope of the line that is perpendicular to a line with the equation:

Explanation

Lines can be written in the slope-intercept form:

In this equation, is the slope and is the y-intercept.

Lines that are perpendicular to each other have slopes that are negative reciprocals of each other. This means that you need to flip the numerator and denominator of the given slope and then change the sign.

First, find the reciprocal of :

Flip the numerator and the denominator.

Next, change the sign.

7

varies inversely as the square root of . If , then . Find if (nearest tenth, if applicable).

Explanation

The variation equation is for some constant of variation .

Substitute the numbers from the first scenario to find :

The equation is now .

If , then

8

Given the line 4y = 2x + 1, what is the slope of this line?

1/2

1/4

–1/4

–2

2

Explanation

4y = 2x + 1 becomes y = 0.5x + 0.25. We can read the coefficient of x, which is the slope of the line.

4y = 2x + 1

(4y)/4 = (2x)/4 + (1)/4

y = 0.5x + 0.25

y = mx + b, where the slope is equal to m.

The coefficient is 0.5, so the slope is 1/2.

9

Find the slope of the coordinates.

Explanation

To find slope, it is differences of the -coordinates divided by the differences of the coordinates.

10

Find the slope of the line that passes through the following points:

and

Explanation

Use the following formula to find the slope:

Remember that points are written in the following format:

Substitute using the given points:

Simplify.

Since you cannot divide by , the slope of this vertical line is undefined.

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