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 . If you selected two points and did get a value of  for the slope, make sure you select two points that are on the line. 

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 . If you selected two points and did get a value of  for the slope, make sure you select two points that are on the line. 

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  we can subtract  from both sides:

Now that we have the slope and the y-intercept, we can plug those values in for  and 

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 ; thus, his weight changes by  each month.

The time is displayed along the x-axis of the provided graph. Between the  and the  period of the race, the driver is going  at each time point. We can see from the straight line between those two points that the race car driver's speed doesn't change; thus, the race car driver is driving at a consistent speed. 

The time is displayed along the x-axis of the provided graph. During the last  of the race, the driver goes from , displayed on the y-axis of the graph, to . We can see the line between those two points is decreasing in a negative direction, or getting slower; thus, the race car driver is decreasing his speed. 

The time is displayed along the x-axis of the provided graph. During the first  of the race, the driver goes from , displayed on the y-axis of the graph, to . We can see the line between those two points is increasing in a positive direction, or getting faster; thus, the race car driver is increasing his speed. 

When the time is at , displayed along the x-axis, we see that the speed, displayed along the y-axis is also . If a car has a speed of , the car is not moving. And if the time is at , the race has not started; thus, the race car driver is waiting to begin the race. 

The time is displayed along the x-axis of the provided graph. During the first  of the race, the driver goes from , displayed on the y-axis of the graph, to . We can see the line between those two points is increasing in a positive direction, or getting faster; thus, the race car driver is increasing his speed. 

The time is displayed along the x-axis of the provided graph. Between the  and the  period of the race, the driver is going  at each time point. We can see from the straight line between those two points that the race car driver's speed doesn't change; thus, the race car driver is driving at a consistent speed.

The time is displayed along the x-axis of the provided graph. During the last  of the race, the driver goes from , displayed on the y-axis of the graph, to . We can see the line between those two points is decreasing in a negative direction, or getting slower; thus, the race car driver is decreasing his speed.