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:

Question

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).

Answer 1

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