Review - Linear Equations

Finding Slope of a Line

100

Identify the slope of the following equation. y = mx + b

the variable m

200

Identify the slope of the following equation. y = 2x + 3

slope is 2

300

Name three ways to describe slope.

Possible answers: 

rate of change 

rise over run

slope = m in y = mx + b

(y₂-y₁)/(x₂-x₁₎

400

Find the slope of the line that includes the following points. (4, -5) (-4, 5)

-10/8 which simplifies to -5/4

500

Find the slope of the line that includes the following points. (-12, -9) (-3, -3)

-6/-9 = 6/9 = 2/3

Direct Variation

100

The value of x varies directly with y, If y is 24 when x is 6, what is the value of y when x is 16?

64

200

If I pay $6.19 for 2 gallons of gas, how much will I pay for 15 gallons? (rounded to the nearest cent)

$46.43

300

If I plant 4 flowers within a plot of 3 square feet, how many square feet of soil do I need to prepare to plant 60 flowers?

45 square feet

400

Rolando gets paid $7.45 per hour. If he works 5 hours on Tuesday, how much money did he make on Tuesday?

$37.25

500

Maria writes 4 letters every week to family members who live far away. How many letters does she write in 32 days? (round to the nearest whole letter)

18

Writing Equations

100

If I am given two coordinate points, what are the steps I take to write an equation in slope-intercept form for the line?

1. Label Points

2. Plug values into slope formula (y₂-y₁)/(x₂-x₁) to find the slope.

3. Plug the evaluated slope and one point into point-slope formula

4. Solve for y (or convert to slope-intercept form)

200

Write an equation for a line that goes through the point (0, 16) with a slope of 3.

y = 3x + 16

300

Write an equation for a line with the following slope and coordinate pair: 

m= -4

(-11, 2)

y = -4x - 42

400

What is the equation in standard form that passes through the point (-2, 12) and has a slope of 3?

-3x + y = 18

500

The amount y(in dollars) of money you have left after playing x games at a carnival is y = -0.75x + 10. How much money do you have after playing eight games? Graph the equation and show your explanation.

y = -0.75(8) + 10

y = -6 + 10

y = 4

$4 dollars left after playing 8 games.

Slope-Intercept Form

100

What is slope intercept form?

y = mx + b

200

In the following linear equation, what is the y-intercept? y = -3/4x

0

300

Rewrite this equation in slope-intercept form. 

y - 5 = 3(x + 2)

y = 3x + 11

400

Rewrite the following equation in slope-intercept form. 3x + 6y = -18

y = -1/2x - 3

500

Rewrite the following equation in slope-intercept form. 3.5x - 7y = -21

                        -7y = -3.5x + 21 

so...

                 y = 0.5x - 3 or y = 1/2x - 3

Parallel and Perpendicular Equations

100

What is the slope of a line parallel to y = 2/3x - 17 ?

2/3

200

What is the slope of a line perpendicular to y=-5x + 3 ?

1/5

300

What is the equation of a line that passes through the point (5, -3) and is parallel to y= 6x - 2 ?

y = 6x - 33

400

What is the equation of a line that passes through the point (-5, -7) and is perpendicular to y=5x + 25?

y = -1/5x - 8

500

Write two equations:

1) an equation for a line that is parallel to y= 2x+ 1 and includes the point (3, 4)

2) an equation for a line that is perpendicular to y = 2x + 1 and includes the point (3,4).

1) y = 2x - 2

2) y = -1/2x + 11/2