Mini Lesson Question
Question #3: Interpret Slope and y-Intercept
Interpret Slope and -Intercept
Many real-world applications are modeled by linear equations. Often, when a linear equation model uses real-world data, different letters are used for the variables, instead of using only and . The variable names remind us of what quantities are being measured.
The equation is used to estimate the temperature in degrees Fahrenheit, , based on the number of cricket chirps, , in one minute. The graph shows the relationship.
What do the slope and -intercept represent?
Answer: The slope is and represents that for every 4 chirps per minute, the temperature increases by 1 degree. The - intercept means when there are zero chirps, the temperature is 40 degrees.
Try it
Try It: Interpret Slope and -intercepts
Loreen has a calligraphy business. The equation models the relation between her weekly cost, , in dollars and the number of wedding invitations, , that she writes. The graph shows the relationship.
What do the slope and -intercept represent?
Here is how to interpret the slope and -intercept:
The slope is 1.8 and represents the cost increases by $1.80 for 1 invitation. The -intercept means the cost for zero invitations is $35.
Check Your Understanding
Sam drives a delivery van. The equation models the relation between his weekly cost, , in dollars and the number of miles, , that he drives. The graph shows the relationship.
Find and interpret the meaning of the slope and -intercept.
Multiple Choice:
The slope, 0.5, means that the weekly cost, C, increases by $0.50 when the number of miles driven, m, increases by 1. The C-intercept means that when the number of miles driven is 0, the weekly cost is $60.
The slope, 0.5, means the weekly cost, C, increases $0.50 a week. The C-intercept is 60, which means that every mile costs $60.
The slope, 0.5, means that for every half mile, m, the cost, C, increases by 1. The C-intercept means that when the number of miles driven is 0, the weekly cost is $60.
The slope, 0.5, means that the weekly cost, C, decreases by $0.50 when the number of miles driven, m, increases by 1. The C-intercept means that when the number of miles driven is 60, the weekly cost is $0.
The slope, 0.5, means that the weekly cost, 𝐶 , increases by $0.50 when the number of miles driven, 𝑚 , increases by 1. The 𝐶 -intercept means that when the number of miles driven is 0, the weekly cost is $60.
For every mile that Sam drives, the cost increases $0.50. The weekly cost is the 𝐶 -intercept which is $60, when zero miles are driven.
Videos: Interpreting Slope and y-Intercept of Linear Equations
Khan Academy: Slope, -Intercept, and -Intercept Meaning in Context
Watch the following video to see how you can interpret slope, -intercept, and -intercept in context.
Khan Academy: Slope and Intercept Meaning in Context
Watch this video to see how you can interpret slope and intercept meaning in context.