Note: As you may have unintentionally missed to attach the figure. After a little research, I was able to find the figure. I have attached the figure, based on which I am solving which anyways would clear your concepts.
Answer:
Part a) The equation of the line, written in slope-intercept form
[tex]y=-40x+160[/tex]
Part b) When Josh starts, he is 160 miles away from his house.
Part c) Josh is travelling at the sped of 40 miles per hour, as the slope of linear equation as the speed.
Step-by-step explanation:
Part A) What is the equation of the line, written in slope-intercept form? Show how you determined the equation.
From the attached figure it is easy to determine
As the slope formula is
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Substituting the intercepts points as
[tex]\left(x_1,\:y_1\right)=\left(0,\:160\right),\:\left(x_2,\:y_2\right)=\left(4,\:0\right)[/tex]
[tex]m=\frac{0-160}{4-0}[/tex]
[tex]m=-40[/tex]
As the slope is negative, it means the function must be decreasing.
As the slope-intercept form is
[tex]y=mx+b[/tex]
From here, we see that
[tex]m=-40[/tex], [tex]b\:=\:160[/tex]
Therefore, the equation of the line, written in slope-intercept form
[tex]y=-40x+160[/tex]
Part B) Based on the linear model, predict how far Josh is away from home when he starts?
As the y-intercept is found when x = 0. So, the coordinates of y-intercept as (0, 160).
As from the graph is it clear that y - intercept is (0, 160).
It means,
for x = 0 hours, the miles are y = 160
Thus, when Josh starts, he is 160 miles away from his house.
Part C) Approximately how fast is he traveling on his trip?
As we know that the speed is determined by dividing the distance over a time.
Or the speed can also be calculated using the formula
[tex]speed\:=\:\frac{distance}{time}[/tex]
Here, the slope also represents the speed, as slope is defined by finding the ratio of the 'vertical change' to the 'horizontal change' between (any) two distinct points on a line.
Therefore, Josh is travelling at the sped of 40 miles per hour, as the slope of linear equation as the speed.
Keywords: slope, speed, slop-intercept form, line of equation
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