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Linear equations
Word Problems
100
State whether the ordered pair is a solution to the equations.


x - 2y = 6

(0, -3)

yes
100
Find the slope of the line.


y = 5x + 7

m = 5
100
Find the equation of the horizontal line through the point (-1, 6)
y = 6
100
Which of these are linear equations?


2x + 4y = 5 ;  .3x = y ; x(squared) + 3y = 12;

 y = 1/x - 7

2x + 4y = 5 and .3x = y
100

Kim and Cyndi are starting a business tutoring students in math. They rent an office for $400 per month and charge $40 per hour per student. Write an equation for this situation.

x = # hours

y = 400 + 40x

200
State whether the ordered pair is a solution of the equations.


-3x + 4y = -7

(2, -1/4)

yes
200
Find the slope of the line through the points (2, 1) and (4, 9)
m = 4
200
Find the equation of the vertical line through the point (-3, 6)
x = -3
200
Write the equation in slope intercept form


y - x = 7

y = 1x+7
200

At a school play, children’s tickets cost $3 each and adult tickets cost $7 each. The total amount of money earned from ticket sales equals $210. Write a linear model that relates the number of children’s tickets sold to the number of adult tickets sold.

3x + 7y = 210
300
Names two solutions to the given equation.


y = -x

examples:  (0, 0) (1, -1) (-1, 1)
300
Find the slope of the line x - 3y = -2
m = 1/3
300
Find the equation of the line through the point (2, -3) and parallel to y = x - 10
y = x - 5
300
Write the equation in standard form.


y = 14 - 3x


3x + y = 14
300

Lin is tracking the progress of her plant’s growth. Today the plant is 5 cm high. The plant grows 1.5 cm per day. Write a linear model that represents the height of the plant after d days.

h = 5 + 1.5d
400
What is the x-intercept and the y-intercept of the given equation.


4x + y = 20

x-intercept (5,0)

y-intercept (0, 20)

400
Find the slope of the line.

x = 3/5

undefined
400
Find the equation of the line through the points

(0, -8) and (-1, -2) 

y = -6x - 8
400
Write the equation in standard form.


y = 4x - 18

4x - y = 18
400

Mr. Thompson is on a diet. He currently weighs 260 pounds. He loses 4 pounds per month. Write a linear model that represents Mr. Thompson’s weight after m months.  What does the slope and y-intercept in the equation represent?

y = 260 - 4m


slope = amount he loses per month

y-int =  his intital weight

500
Is (4, 7) a solution to the equation y = 9?
no
500
Find the slope of the line perpendicular to the line 

y - x = 1

m = -1
500
Find the equation of the line parallel to 2x + y = 2 and having the same y-intercept as 3x + 4y = 12
y = -2x + 3
500
Write the equation in standard form.


y = 3/2 x + 5

3x - 2y = -10
500

Kara used the linear model y = 20,000 + 0.3x to predict her total salary from achieving total sales of x. What is her base salary? What percent commission does she earn?

Base salary = $20,000.

Percent commission = 30%