Question

Hi! I really need help on this ASAP please. If you're able to answer this, thank you! :')

Heather ran a race at a constant rate. The table shows the time she reached each mile marker.

Let X represent the mile marker reached and let y represent the overall time passed.

Mile Marker: 0 | 1 | 2 | 3
Time (min): 0 | 8 | 16 | 24

(a) Write the equation in point-slope form to represent the mile reached over time
(b) Find the total time it will take Heather to run a 9-mile race if she maintains the same rate. Explain your reasoning.

Answer 1

Answer:  

y − 8 = m(x − 1)

72 minutes

Step-by-step explanation:

Point slope form is:  y − y1 = m(x − x1)

Pick any two points.  I'll pick (1,8) and (2,16).  I will make the first point the (x1,y1) we need for the point slope equation:

y − y1 = m(x − x1)

y − 8 = m(x − 1)

We can calculate the slope, m, by determining the Rise/Run of the line.  The Rise is the change in y for the Run, the change in x.

Change in Run (x) = (2-1) = 1

Change in Rise (y) = (16-8) = 8

Slope (Rise/Run) = 8

m is 8

y − 8 = m(x − 1)

y − 8 = 8(x − 1)

or

y = 8x

We can now predict Heather's time to complete the 9 miles:

y = 8x

y = 8*(9)

y = 72 minutes