Review the concepts of slope and y-intercept, and think about the information they give.
See solution.
Practice makes perfect
To find the corresponding interpretation of the slope and y-intercept for a real-world application, it will be useful to review each concept first. Then we can interpret them accordingly.
Slope interpretation
For a linear function, the slope is the ratio between the rise and run for any two points in the graph. The run is the difference in the x-values of two points on the line, while the rise is the difference in the y-values of two points on the line. We can define the slope as shown below.
Slope &=Rise/Run= Change iny-values/Change inx-values
For a real-world situation, the slope is the rate between the change in the y quantity and the x quantity. Depending on the context, it may have a special interpretation. For example, in a graph for position versus time the slope would be the change in the position per unit of time. The slope is the velocity of the object!
y-intercept interpretation
The y-intercept is the y-coordinate of the point where the line intersects the y-axis. The x-coordinate for the point where this happens is always 0. Therefore, this usually represents the initial value for the situation we are modeling.
