Amari is researching an electric car. He finds this graph, which shows how much range, measured in kilometers, the car gains based on charging time:
km = 105 min = 10
km = 300 min = 20
km = 405 min = 30
Amari want an equation he can use to find how much charging time (t) it takes to gain any number of kilometers in range (k).
We can solve this problem using the method of solving systems of linear equations. Let's first list the given data in the form of points (t, k):
(10, 105)
(20, 300)
(30, 405)
Let the equation be in the form k = mt + b, where m is the slope, t is the charging time, and b is the y-intercept.
First, we need to find the slope (m). We can do this using any two points, but let's use points (10, 105) and (20, 300) for simplicity. The slope is given by:
m = (k2 - k1) / (t2 - t1)
Plugging in the values from the points:
m = (300 - 105) / (20 - 10)
m = 195 / 10
m = 19.5
Now we have the slope, we can find the y-intercept (b) using any point (t, k). Let's use point (10, 105) for simplicity:
k = mt + b
Plugging the known values of m, t, and k:
105 = 19.5(10) + b
Now solve for b:
b = 105 - 195
b = -90
Now we have the slope (m) and y-intercept (b), we can write the equation as:
k = 19.5t - 90
So the equation Amari can use to find out how much charging time it takes to gain any number of kilometers in range is:
k = 19.5t - 90