Writing Linear Functions
Graphing Linear Functions
Slope
Linear Functions Word Problems
Function Notation
100
A linear function has a slope of -3 and passes through the point (2,-2).
Write the equation of the line in slope-intercept form.
y=-3x+4
100
Which point lies on the graph of y = 2x − 1?
(-2, -4) or (0, -1)?
(0, -1)
100
y=3x+2
100
Miguel measure the shadow of a meter stick to be 125 cm and the shadow of 12 cm marker to be be 15 cm.
Write an equation that gives the shadow length (in cm) to the object's height (in cm).
y - 15 = 1.25(x - 12)
or y - 125 = 1.25(x - 100)
or y = 1.25x
100
If f(x) = 2x - 17, determine its x-intercept (when f(x) = 0).
(8.5, 0)
200
What is the linear equation?
y=3x+3
200
Is there a y-intercept of the graph x = 4, and if so, what is it? Explain.
No, x=4 is a vertical line that does not lie on the y-intercept
200
Find the slope of a line that passes through the points (0, 5) and (2, 10)
y=5/2x+5
200
An attorney charges a fixed fee of $250 for an initial meeting and $2.50 per minute for all minutes worked after that.
a) If an equation is written in slope intercept form, what is the value of "b" (y-intercept) and what does it represent?
b) You meet with the attorney for 1 hour, using the information above, how much will the attorney charge?
a) b = $250 and it is the fixed fee charged by the attorney
b) $400
200
If g(x) = 28 - 4x, then determine g(-2).
g(-2) = 36
300
Write the linear function in this graph:
y=20x-15
300
The given table shows a linear function.
What is the missing number in the table? HINT: think rise/run
x 0 2 4 6
y -1 1 ? 5
3
300
What is the slope of the linear function
y = 14
0
300
A video streaming app charges a $9 membership fee and $1.50 for each video stream.
a) Write a linear equation in slope-intercept form to model this scenario.
b)How much would it cost to stream 12 videos?
a) y=1.50x + 9
b) $27
300
If h(x) = 24 + x/2, then determine for what x-value h(x) = -24 .
x = -96
400
Write a linear function that passes through the points (0,2) and (-4,5).
y= 3/4x +2
400
Given 5x - 2y = 20, find the x & y intercepts
x-intercept is (4, 0)
y-intercept is (0, -10)
400
Find the slope of a linear function that contains the points (-2 , 8) and (5 , -13)
-3
400
A water tank already contains 55 gallons of water when Baxter begins to fill it. Water flows into the tank at a rate of 8 gallons per minute.
a) What is the equation?
b) How long will it take to get to 95 gallons in the tank?
a) y=8x +55
b) 5 minutes
400
If g(x) = 28 - 4x and j(x) = 6x - 23, then determine the value of x where g(x) = j(x).
x = 5.1
500
Write x-2y=-4 in slope intercept from.
y=0.5x+2
500
Convert the equation below to slope intercept form
-2x + 3y = 12
y = 2/3x + 4
500
What is the slope of the line with equation x = -7?
Undefined.
500
You are at school, 12 miles away from home. You start walking home with your friends at a speed of 3 miles per hour towards your home.
a. Write an equation that represents your distance from home (y) after (x) hours.
b. How many hours does it take to get home?
a. y = -3x + 12 or y = 12 - 3x
b. 4
500
If k(x) = 28 - 8x and w(x) = 5x - 20, then determine a) the sum of their y-intercepts
b) which function is the steeper line?
a) sum of the y-intercepts = 8
b) k(x) is steeper