Question

Josh is on a road trip returning home from vacation. The graph below showst shows distance remaining at various times on the trip. (a) What is the equation of the line, written in slope-intercept form? Show how you determined the equation. (b) Based on the linear model, predict how far Josh is away from home when he starts?. Approximately how fast is he traveling on his trip?

Answer 1

Answer:

Part a) $y=-40x+160$

Part b) see the explanation

Part c) $40\ \frac{miles}{hour}$

Step-by-step explanation:

The picture of the question in the attached figure

Let

x ----> the time in hours

y ----> the number of miles from Josh's home

Part a) What is the equation of the line, written in slope-intercept form?

step 1

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

take the intercepts points

(0.160) and (4,0)

substitute

$m=\frac{0-160}{4-0}$

$m=\frac{-160}{4}=-40$

The negative slope means that the function is decreasing

step 2

Find the equation of the line

$y=mx+b$

we have

$m=-40\\b=160$

$y=-40x+160$

Part b) Based on the linear model, predict how far Josh is away from home when he starts?

we know that

The y-intercept is the value of y when the value of x is equal to zero

Looking at the graph

For x=0

y=160 miles

therefore

When Josh starts, he's 160 miles away from his house.

Part c) Approximately how fast is he traveling on his trip?

Remember that the speed is equal to divide the distance by the time

In this problem, the slope of the linear equation is the same that the speed

so

$40\ \frac{miles}{hour}$