Cameron stops to get gas soon after beginning a road trip. He checks his distance from home 2 hours after filling his gas tank and checks again 3 hour

sagnuhh

sagnuhh

Answered question

2021-01-31

Cameron stops to get gas soon after beginning a road trip. He checks his distance from home 2 hours after filling his gas tank and checks again 3 hours later. The first time he checked, he was 170 miles from home. The second time, he was 365 miles from home. What equation models Cameron's distance from home as a function of the time since getting gas?

Answer & Explanation

Theodore Schwartz

Theodore Schwartz

Skilled2021-02-01Added 99 answers

Let x represent the number of hours since beginning the road trip and y be the distance from home in miles.
Two points in the situation are (2,170) for 2 hour later and (5,365) for 3 hours later (Note: 2+3=5hr). Using these points, the slope is:
m=y2y1x2x1=36517052=1953=65
Using this slope and either of the two points (I used (2,170)) to the slope-intercept form of a line, we solve for b:
y=mx+b
170=65(2)+b
170=130+b
40=b
So, the equation is: y=65x+40

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