Write an equation in point-slope form, and find which high marker he will pass 90 minutes after crossing Sandy River.

Question

Michael was driving at a constant speed of 60 mph when he crossed the Sandy River. After 1 hour, he passed a highway marker of mile 84. Write an equation in point-slope form, and find which high marker he will pass 90 minutes after crossing Sandy River.

Answer 1

y=mx+b is the slope-intercept form if you need it

y=60(x-1)+84 where x is the amount of time in hours and 90 minutes=1.5 hours

y=60x-60+84

y=60x+24

y=60(1.5)+24

y=90+24

y=114

highway marker mile 114

Don't forget that after 1 hour (or 60 minutes) he passed marker 84. Ninety minutes after crossing Sandy River is only 30 minutes more time than 60 minutes. We want the mile marker 30 minutes after passing marker 84.

Going 60 mph is 1 mile per minute. Thirty minutes later he travels another 30 miles past marker 84, so he is at marker 84+30=114. 

Answer 2

Hi Tom;

x-axis is quantity of miles.  Because he is traveling at 60 miles/hour, 1 mile/minute, no additional calculations are necessary.

y-axis is markers

(x₁,y₁).....(60 miles, mile-84)

(x₂,y₂).....(90 miles, mile-(84+30))...(90 miles, mile-114)

Point-slope formula...

y-y₁=m(x-x₁)

m is slope.

Slope is change-of-y divided by change-of-x...

m=(y-y₁)/(x-x₁)

m=(114-84)/(90-60)

m=30/30

m=1

y-y₁=m(x-x₁)

Let's input one point.  I randomly select the second...

y-114=1(x-90)

y-114=x-90

Add 114 to both sides...

y=x+24

Let's input the other point to verify results...

y-y₁=m(x-x₁)

y-60=1(x-84)

y-60=x-84

Add 60 to both sides...

y=x+24

 

It is no coincidence that 84-60=24.