You can use point-slope form. How does the volume change over the hours?
Equation: y=-60x+480 Example interpretation: The volume decreases by 60cubic feet each hour.
Practice makes perfect
We are given a graph showing how the volume of a swimming pool changes over time. Since we are given two points on the line, it will be most convenient to use point-slope form.
Equations in this form follow a specific format.
y- y_1= m(x- x_1)
In this form, m is the slope of the line and ( x_1, y_1) is a point on the line. We need to identify these values using the graph. Let's start with the slope.
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 (5,180) from the point (3,300) requires that we move 2 steps horizontally in the positive direction and 120 steps vertically in the negative direction.
rise/run=-120/2=-60 ⇔ m= -60
The slope of -60 tells us that the volume decreases by 60cubic feet each hour.
Writing the Equation
Now that we know that the slope of the line is -60, we can write the equation of the line in point-slope form. We can use either of the given points as (x_1,y_1) in our equation. Let's use ( 3, 300).
While this is a valid format for the equation of the line, we can rewrite it in the slope-intercept form so that we can have the unique equation for the line.
