Answer:
Part a) [tex]y=-40x+160[/tex]
Part b) see the explanation
Part c) [tex]40\ \frac{miles}{hour}[/tex]
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
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take the intercepts points
(0.160) and (4,0)
substitute
[tex]m=\frac{0-160}{4-0}[/tex]
[tex]m=\frac{-160}{4}=-40[/tex]
The negative slope means that the function is decreasing
step 2
Find the equation of the line
[tex]y=mx+b[/tex]
we have
[tex]m=-40\\b=160[/tex]
[tex]y=-40x+160[/tex]
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
[tex]40\ \frac{miles}{hour}[/tex]
