Answer:
The linear equation in slope intercept form that relates the height y of the ramp to he distance x from the curb is:
[tex]y=\dfrac{-1}{5}x+11[/tex]
Step-by-step explanation:
If we model this equation on a coordinate plane we see that the ramp passes through the point (0,11) and (55,0)
where the horizontal axis i.e. the x-axis represent the distance of the ramp from the curb and the vertical axis represent the height y of the ramp.
We know that the ramp satisfies a linear relationship.
Hence, the slope is constant between two points.
i.e. the slope of a line passing through (a,b) and (c,d) is calculated by:
[tex]Slope=\dfrac{d-b}{c-a}[/tex]
Also, the slope intercept of a line is given by:
y=mx+b
where m is the slope and b is the y-intercept.
From the given problem we have slope as:
[tex]m=\dfrac{0-11}{55-0}\\\\\\m=\dfrac{-11}{55}\\\\\\m=-\dfrac{1}{5}[/tex]
Also, y-intercept is: b=11
( Since the y-intercept is the value where x=0 )
The equation is given as:
[tex]y=\dfrac{-1}{5}x+11[/tex]
