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 y = (1/2)x + 1 , find the value of y when x=8.
y = 5
Find the midpoint M(x, y) of the line segment joining these pairs of points.
a (1, 0) and (4, 4)
b (−3, −2) and (5, 3)
M = (2.5, 2)
M = (1, 0.5)
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 equation of a line whose slope is 3 and passes through the point (0,1).
y = 3x + 1
Given y = -2x - 7, find the value of x if y = 11
x = -9
Find the length of the segment joining (−2, 2) and (4, −1), correct to two decimal places.
c = sqrt45
∴ length = 6.71 units (to 2 d.p.)
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
Find the equation of a line whose y-intercept is -6 and passes through the points (-1, 2)?
y = -8x - 6
Given the points (5, 1) and (8, -2) on a line, find the slope.
m = -1
If two lines are parallel then they have the same gradient. Find the equation of a line which is parallel to y = 3x − 1 and passes through (0, 4) .
y = 3x + 4
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 the line which passes through Point A: (-5, 15) Point B: (0, 10)
y=-x+10
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
If two perpendicular lines (at right angles) have gradients m1 and m2 then:
m1 × m2 = −1 or m2 = − 1 /(m1)
Find the equation of a line which is perpendicular to the line y = 2x − 3 and passes through (0, −1).
y = − 1/ 2 x − 1
The temperature when I woke up at 8AM was 18 degrees. At 1 PM, the temperature was 28 degrees. Write a linear equation that models the temperature F, with respect to the time of the day, h hours after midnight.
F = 2h + 2
Solve: 4x - 3(2x - 1) = -2x - 5
No solutions (lines are parallel)
Write the equation of a line passing through the points (1, 5) and (-2, -1)
y = 2x+3
If f(x) = (3/4)x + 6, find the x-intercept.
x = -8
Solve y = 3x - 2
y=-x+2
(1,1)
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