Question

a wooden access ramp is being built to reach a platform that sits 60 inches above the floor. the ramp drops 4 inches for every 29 - inch run.
(a) write a linear equation that relates the height y of the ramp above the floor to the horizontal distance x from the platform.
y = -\frac{4}{29}x + 60
(simplify your answer. use integers or fractions for any numbers in the expression.)
(b) find and interpret the x - intercept of the graph of your equation.
the x - intercept is 435.
(type an integer or a fraction.)
now interpret the x - intercept of the graph of your equation. choose the correct answer below.
a. the ramp meets the floor this many inches from the base of the platform.
b. the maximum rise is this many inches.
c. the ramp meets the platform this many inches from the floor.
d. the length of the ramp is this many inches.

Explanation:

Step1: Write the linear - equation

The ramp drops 4 inches for every 29 - inch horizontal change. The platform is 60 inches from the point of vertical - height measurement. The slope $m=-\frac{4}{29}$, and using the point - slope form $y - y_1=m(x - x_1)$, with the point $(x_1,y_1)=(0,0)$ (assuming the start of the ramp at the platform level as the origin), the linear equation is $y =-\frac{4}{29}x + 60$.

Step2: Find the x - intercept

Set $y = 0$ in the equation $y=-\frac{4}{29}x + 60$. Then $0=-\frac{4}{29}x+60$. First, add $\frac{4}{29}x$ to both sides: $\frac{4}{29}x = 60$. Then multiply both sides by $\frac{29}{4}$ to solve for $x$. So $x=60\times\frac{29}{4}=435$.

Step3: Interpret the x - intercept

The x - intercept represents the horizontal distance from the platform where the ramp meets the floor.

Answer:

(a) $y =-\frac{4}{29}x + 60$
(b) The x - intercept is 435. It means the ramp meets the floor 435 inches from the base of the platform.