Linear Equations
Write the equation of a line with a slope of -2 and a y-intercept of 3
What is y = -2x + 3?
Given g(x) = (1/2)x + 1, find the value of g(8).
g(8) = 5
Solve y = 3x - 2
y=-x+2
(1,1)
You start a new job that pays you $15 per hour. Write an equation that represents your earnings, E, after h hours of work.
E = 15h
Does the point (6, -2) lie on the graph of
y = -(1/2)x - 1?
No
What is the x value of the point (3, -5).
What is x = 3?
Given y = -2x - 7, find the value of x if y = 11
x = -9
This graph would be shaded _______: y > -x + 4
above
A person initially weighs 180 pounds. After 2 months, the person's weight is now 166 pounds. Write a linear equation that models the person's weight loss. Let W represent the weight of the person, and m the number of months.
W = -7m + 180
For the function f(x) = 7x - 2, which of the following is true?
(A) The slope is 7x and the y-intercept is -2
(B) The slope is 7 and the y-intercept is -2
(C) The slope is -2 and the y-intercept is 7x
(D) The slope is -2 and the y-intercept is 7
B
What is the equation of a line whose slope is 3 and passes through the point (0,1).
y = 3x + 1
Given the points (5, 1) and (8, -2) on a line, find the slope.
m = -1
This graph would have a ______ line and shade ______ 2y >= 3x - 10
solid, above
A person finances a new car and needs to pay off the balance of $15,000. The payment plan for the car is $250 per month. Determine how many YEARS it will take for the balance on the car to be $6000.
3 years
The profits for a business at the start of the new year can be modeled by P(I) = 325I + 5000, where I is the number of items sold and P(I) is the profit in dollars. Give an interpretation of the parameters 325 and 5000.
325: For every item sold, profits increase by $325
5000: The starting profit for the year was $5000 (0 items have been sold)
Find the equation of a line whose y-intercept is -6 and passes through the points (-1, 2)?
y = -8x - 6
A population of deer can be modeled by the equation D = 5m + 72. A population of rabbits in the same area can be modeled by the equation R = 12m + 30. Find after how many months the populations of both the deer and rabbits will be the same.
6 months
This graph would shade _______: -5y + 10x - 15 > 0
below
The temperature when I woke up at 8AM was 65 degrees Fahrenheit. At 12 PM, the temperature was 77 degrees Fahrenheit. Write a linear equation that models the temperature F, with respect to the time of the day, h hours after midnight.
F = 3h + 41
Solve: 4x - 3(2x - 1) = -2x - 5
No solutions (lines are parallel)
Write the equation of a line passing through the points (-4, -7) and (0, -1/3)
y = (5/3)x - 1/3
If f(x) = (3/4)x + 6, find the x-intercept.
x = -8
Solve the inequality 3x - 4 > 2(x + 2)
x > 8
Larry just opened up a bank account. His starting balance was $30. Every week, he deposits $125 from his work paycheck into his bank account.
Larry is saving up for a new Macbook Pro that costs $1780. How many weeks will he need to save for?
w = 14
The slope between the points (-3, 5) and (9, a) is -2/3. Find the value of a.
a = -3