Common Core: 8th Grade Math : Construct and Find the Rate of Change of a Function Model: CCSS.Math.Content.8.F.B.4
Study concepts, example questions & explanations for Common Core: 8th Grade Math
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Example Questions
Example Question #61 : Functions
What is the function that represents the graph provided?
A function is represented by an equation. When making our equation, we need to know the rate of change, or the slope, and the y-intercept, which is the initial value or starting point.
Remember, the rate of change, or slope, is a rate that describes how one quantity changes in relation to another. To find the rate of change, or slope, we can use the following formula:
In a graph, we need to find two sets of coordinate points in order to solve for the rate of change, or slope. Looking at our graph, let's pick the following points:
We can plug these points into the formula for slope, and solve for the rate of change:
The rate of change, or slope, for the provided graph is 
*Important note: Any two points selected from the graph of the line will equal a slope of 
Now that we have our slope, we can use our known values and solve for the y-intercept, or the initial value.
Remember, the equation of our line will be in slope-intercept form:
Plug in the slope and a set of coordinate points from the graph provided in the question:
To solve for 
Now that we have the slope and the y-intercept, we can plug those values in for 
Example Question #62 : Functions
When Tim was born he weighed 
Remember, the rate of change is a rate that describes how one quantity changes in relation to another. If we were given a table, the rate of change would be described as followed:
If we were given a graph, then the rate of change would be the slope of the line in the graph. It could be calculated by using the formula:
For this situation, we have an initial value and a rate of change.
The initial value is the weight that Tim started at:
The rate of change is how much he gained each month. Each month he gained 
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