Writing Linear Functions
Graphing Linear Functions
Slope
Linear Functions Word Problems
Sequences
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 measures 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
What is an arithmetic sequence?
A pattern of numbers that is being added or subtracted by the same number.
200
What is the linear equation that is perpendicular to the graphed equation and goes through the (3,12) ?
y=-1/3x+13
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
What is the difference between recursive formula and explicit formula?
Recursive - finds the number before
Explicit - find any nth term
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
Bill purchased monthly video streaming app. One the first month, he was charged for streaming 10 videos. The 2nd month he was charged $34.50 for 17 video streams.
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
Find the 35th term in the sequence.
-8, -1, 6, 13, 20, .....
230
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
Braxton needs to fill a water tank. After 10 minutes the tank had 135 gallons of water. The tank needed more water so after 21 minutes it now has 223 gallons of water. If Braxton continued for 1 hour, how much water is in the tank?
a) What is the equation?
b) How much water is in the tank after an hour?
a) y=8x +55
b) 535 gallons
400
Using the recursive formula, find the 22nd term in the sequence.
45
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
a) If the 14th term in a sequence is -29 and has a common difference of losing 2, what was the first term?
b) What is the 8th term?
a) -3
b) -17