Question

Aniyah is driving home at a constant speed. After 20 minutes, she is 70 miles from home. What equation models her distance from home, y, as a function of time, x?

Answer 1

The equation that models her distance from home, y, as a function of time, x will be:

• y = 3.5x

Explanation:

We know that the slope-intercept form of a linear function is

y = mx+b

Here m is the slope and b is the y-intercept

• Please note that slope is also termed as 'rate of change'.

Given that Aniyah is driving home at a constant speed.

at t = 20 minutes, she has covered 70 miles

so the rate of change = 70/20

= 3.5 miles per minute

• Let y be the distance from home

• Let x be the time

Finding the y-intercept by substituting m = rate of change = 3.5 and the point (20, 70)

y = mx+b

70 = 3.5(20) + b

b = 70 - 70

= 0

Thus, the equation becomes

y = mx+b

y = 3.5x + 0

y = 3.5x

Therefore, the equation that models her distance from home, y, as a function of time, x will be:

• y = 3.5x