You can use the slope-intercept form. What is the relation between the amount of fuel and the traveled miles?
Equation: y=-1/30x+12 Example interpretation: For each 1 gallon of gas used, we are able to drive 30 miles.
Practice makes perfect
We are given a graph showing how the amount of fuel in a tank changes over the traveled miles.
Since we are given a y-intercept and a slope, it will be most convenient to use slope-intercept form.
Equations written in this form follow a specific format.
y= mx+b
In this form, m is the slope of the line and b is the y-intercept. We need to identify these values using the graph. Let's start with the y-intercept.
Finding the y-intercept
Observe the given graph.
We can see that the function intercepts the y-axis at (0,12). This means that the value of b is 12.
Finding and Interpreting the Slope
To identify the slope m, let's look at the rise and run of the graph.
Traveling to the point (90,9) from the y-intercept requires that we move 90 steps horizontally in the positive direction and 3 steps vertically in the negative direction.
rise/run=-3/90=-1/30 ⇔ m= -1/30
The slope of - 130 tells us that for each 1 gallon of gas used, we are able to drive 30 miles.
Writing the Equation
Now that we have the slope and the y-intercept, we can form our final equation.
y= mx+b [0.5em]
y= -1/30x+12
