What is the elevation at the bottom of the ski slope?
A
Example Equation: y-800=- 200(x-1)
B
1000feet
C
5minutes, see solution.
Practice makes perfect
We want to write an equation that represents our elevation y (in feet) on a ski slope after x minutes. We are given three ordered pairs that we know are points on the graph of the equation.
x
1
2
3
y
800
600
400
We can use the points in the table to write our equation in point-slope form, where m is the slope of the equation and (x_1,y_1) is one point on the graph of the equation.
y-y_1=m(x-x_1)
First, we use two points to find the slope m. Let's use ( 1, 800) and ( 3, 400) in the Slope Formula.
Next, we substitute - 200 for m and ( 1, 800) for (x_1,y_1) into the general equation for point-slope form. That gives us an equation that represents our elevation y after x minutes.
y-y_1=m(x-x_1) ⇓ y- 800= - 200(x- 1)
Please note that any point on the line can be used in place of (x_1,y_1) so there are many correct equations for this line, ours is just one possible answer.
We want to determine our starting elevation. In Part A we found an equation that represents our elevation y after x minutes.
y-800=- 200(x-1)
In the beginning, the number of minutes is 0. Let's substitute 0 for x in our equation to get the corresponding elevation.
This means that our elevation at the start is 1000 feet.
In this part, we want to decide after how many minutes we reach the bottom of the ski slope. Previously, we found an equation of our elevation y after x minutes.
y-800=- 200(x-1)
When we reach the bottom of the ski slope, our elevation is 0. Therefore, we can substitute 0 for y in our equation to determine how many minutes have passed when we reach the bottom.
It takes 5 minutes to reach the bottom of the ski slope. We can use the graph of our equation to justify our answer. We can rewrite our equation in slope-intercept form to make it easier to draw.
