Interpreting the y-intercept and Slope
y-intercept: The amount of y (dependent variable) at the beginning when x
(independent variable) is 0
Slope: The change of y (dependent variable) for every x
1) Jackson recently bought a computer that came with 30 programs. He added five programs to his computer every month.
a)How many programs were at the beginning (y-intercept)?______
b)How many programs are increasing each month (slope)? ______
The interpretation of the y-intercept is: The amount of programs after 0 months is 30.
The interpretation of the slope: The amount of programs increasing per month is 5.
2) Julie recently purchased a Smartphone that came with 50 songs. She found that she downloaded on average about 5 songs a week.
a) What is the y-intercept (how many are at the beginning)?______
b) Interpret the y-intercept (what does the beginning represent?
______
c) What is the slope (what is the rate of change?) ______
d) Interpret the slope (what is changing and use “per”) ______
3) Mrs. Hudson, a Social Studies teacher, noticed that her students knew about 10 state capitols before she started teaching the unit on State Capitols. For every half-hour that the students studied, they learned 8 more capitols.
a) What is the y-intercept? ______
b) Interpret the y-intercept ______
c) What is the slope? ______
d) Interpret the slope? ______
4) Delaney filled her car’s gas tank with 17 gallons. She noticed that the amount of gas decreased by 1 gallon for every 25 miles she drove.
a) What is the y-intercept? ______
b) Interpret the y-intercept ______
c) What is the slope ______
d) Interpret the slope ______
Example: Write an example that has a y-intercept of 4th floor and a slope of 2 floors per minute. Then interpret the y-intercept and slope.
John exited the elevator on the 4th floor of a building and went to the stairs. He climbed 2 floors each minute. Y-intercept: The floor he was on at the beginning was 4.
Slope: The amount of floors he climbed each minute was 2.
5)Write an example that has a y-intercept of 15 green beans and a slope of 10 green beans per scoop. Then interpret y-intercept and slope. (Do on the back of this paper)
6)Write an example that has a y-intercept of $40 and a slope of $.15 per text after 200 texts (Do on the back of this paper)
7)Create an example that has a y-intercept and a slope. Then write the y-intercept, interpretation of the y-intercept, slope, and interpretation of the slope.
Ideas include: Taxi-ride fare; filling a swimming pool; words per minute that someone can type with lessons etc…
Created by Gregory Fisher, Winston-Salem Forsyth County Schools, 2011