Question

Can someone help me ill do anything for u

Answer 1

Answer:

(a)

$\displaystyle y-12=-3(x-6)$

$\displaystyle y=-3x+30$

(b)

Scott took 27 minutes to deliver the packages

Decreased by 3 each day

Step-by-step explanation:

Equation Of The Line

We can define the equation of the line when we have two sets of data. They can be

• One point and the slope
• Two points
• One point and the y-intercept
• The slope and the y-intercept

(a)

From the graph shown in the figure we can identify two points in the line:

$\displaystyle P(6,12)\ Q(3,21)$

We can now compute the slope of the line

$\displaystyle m=\frac{21-12}{3-6}$

$\displaystyle m=\frac{9}{-3}=-3$

With the slope and the point, we find the equation of the line

$\displaystyle y-12=-3(x-6)$

That was the slope-point form of the line. If we operate and reduce, we have

$\displaystyle y-12=-3x+18$

$\displaystyle y=-3x+30$

This is the slope-intercept form of the line

(b)

Using the model obtained in the part (a), we can predict or evaluate the values for any selected value of x. We are required specifically to find how long did it take Scott to deliver his packages. It can be computed setting x=1

$\displaystyle x=1$

$\displaystyle y=-3+30=27$

Scott took 27 minutes to deliver the packages

Finally, we are required to find how much dis his delivery time decrease by day. That is the exact meaning of the slope, the rate of change of y respect to x. Since we already computed the slope, we state

Scott decreased his delivery time by 3 each day