Algebra - Chapter 5

Linear Functions

100

Does this equation represent a linear function?

Yes or No

2x + 3y = 5

Yes

200

Do the given ordered pairs satisfy a linear function?  Explain

(0,5)  (-2, 3)  (-4, 1)  (-6, -1)  (-8, -3)

Yes, this is a function because the pattern in the x-coordinates is -2 and the pattern for the y-coordinates is also -2.

300

Tell whether the given ordered pairs satisfy a linear function.  Why or why not?

(2, -2)  (-1, 0)  (-4, 1)  (-7, 3)  (-10, 6)

No this is not a linear function because the pattern for the y-coordinates is not consistent.

400

Is this function linear?  Why or why not?

x^2 + 3 = y

No, this is not a linear function because the variable x has a power of 2.

500

Is this function linear?  Why or why not?

x/5 = y/3

Yes, this is a linear function.  The variables are in the top of the fractions and have a power of 1.

Standard Form

100

What is the equation look like for Standard Form?

Ax + By = C

200

What is the x-intercept and y-intercept of the equation?

2x - 4y = 4

x-int. = 2

y-int. = -1

300

Write the equation in Standard Form.

4y + 5x = 2y - 3x + 16

8x + 2y = 16

400

What is the x-intercept and y-intercept of the equation?

y - 3x = -15

x-int. = 5

y-int. = -15

500

What is the x-intercept and y-intercept of the equation?

-2y + x = 2y - 8

x-int. = -8

y-int. = 2

Slope

100

What does the slope formula look like?

(y₂ - y₁) / (x₂ - x₁)

200

What is the slope of a vertical line?

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300

Find the slope of the line that passes through the points (2,7) and (4,4).

-3/2

400

Find the slope of the line that contains the pair of points.

(2,5) and (3,1)

-4

500

Find the slope of the line described by the equation.

8x + 2y = 96

-4

Slope-Intercept Form

100

What does the equation for Slope-Intercept Form look like?

y = mx + b

200

Write the equation that describes the line in Slope-Intercept Form.

slope = 5 and the y-intercept = -9

y = 5x - 9

300

Write the equation in Slope-Intercept Form.

6x + 3y = 12

y = -2x + 4

400

Write the equation that describes the line in Slope-Intercept Form.

slope = 0 and (6, -8) is on the line

y = -8

500

Write the equation in Slope-Intercept Form.

5x - 2y + 6 = 10

y = 5/2 x - 2

Point-Slope Form

100

What does the equation for Point-Slope Form look like?

y - y_{1 =} m (x - x₁)

200

Write an equation in Point-Slope Form for the line with the given slope and the given point.

slope = 1/5 and the point is (2,-6)

y + 6 = 1/5 (x - 2)

300

Write an equation in Point-Slope Form for the line with the given slope and the given point.

slope = -6 and the point is (-8, -10)

y + 10 = -6 (x + 8)

400

Write an equation in Point-Slope Form for the line that goes through these two points.

(1, 1) and (-5, 3)

y - 3 = -1/3 (x + 5)

y - 1 = -1/3 (x - 1)

500

First write an equation in Point-Slope Form for the given information AND then write it in Slope-Intercept Form.

slope = 2 and the line goes through (3, 4)

y - 4 = 2 (x - 3)

y = 2x - 2