Example 1
Suppose an airplane descends at a rate of
300 ft/min from an elevation of 8000 ft.
Write and graph an equation to model the
plane’s elevation as a function of the time
it has been descending. Interpret the
intercept at which the graph intersects the
vertical axis
An equation that models the plane’s
elevation is d = –300t + 8000.
An equation that models the plane’s
elevation is d = –300t + 8000.
The d-intercept is (0,
8000) which means
the plane was at
8000 ft at the
moment it began
its descent.
Example 2
A spring has a length of 8 cm when a 20-g
mass is hanging at the bottom end. Each
additional gram stretches the spring
another 0.15 cm. Write an equation for the
length y of the spring as a function of the
mass x of the attached weight. Graph the
equation. Interpret the y-intercept.
Step 1: Identify the two points
Reminder: mass is defined as x and length as y
(x1, y1) would be the initial information (20, 8)
Adding another 20 g of mass at the end of
the spring will give a total mass of 40 g and
a length of 8 + 0.15(20) = 11 cm. Use the
points (x1, y1) = (20, 8) and (x2, y2) = (40, 11)
to find the linear equation.
Step 3: Use one of the points and the
point-slope form to write an equation
for the line.
The y-intercept is (0, 5).
So, when no weight is
attached to the spring,
the length of the spring
is 5 cm.