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3 years ago

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Starting at the same point, Tom and Juanita go biking in opposite directions. If Tom rides at a speed of 14 mph, and Juanita rid

es at a speed of 20 mph, how far apart will they be in 2 hours?
( Please include explanation, thank you! )

1 answer:

ANTONII [103]3 years ago

7 0

See https://web2.0calc.com/questions/please-help_96053.

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3 years ago

Write the equation of the line that passes through

Gnom [1K]

Answer:

$y=\frac{\displaystyle 1}{\displaystyle 7}x+\frac{\displaystyle15}{\displaystyle 7}$

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Hi there!

Slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x is 0)

<u>1) Determine the slope (</u><u><em>m</em></u><u>)</u>

$m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}$ where two given points are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (-1, 2) and (6, 3):

$m=\frac{\displaystyle 3-2}{\displaystyle 6-(-1)}\\\\m=\frac{\displaystyle 3-2}{\displaystyle 6+1}\\\\\m=\frac{\displaystyle 1}{\displaystyle 7}$

Therefore, the slope of the line is $\frac{\displaystyle 1}{\displaystyle 7}$ . Plug this into $y=mx+b$ :

$y=\frac{\displaystyle 1}{\displaystyle 7}x+b$

<u>2) Determine the y-intercept (</u><u><em>b</em></u><u>)</u>

$y=\frac{\displaystyle 1}{\displaystyle 7}x+b$

Plug in one of the given points and solve for <em>b</em>:

$2=\frac{\displaystyle 1}{\displaystyle 7}(-1)+b\\2=-\frac{\displaystyle 1}{\displaystyle 7}+b$

Add $\frac{\displaystyle 1}{\displaystyle 7}$ to both sides to isolate <em>b</em>:

$2+\frac{\displaystyle 1}{\displaystyle 7}=-\frac{\displaystyle 1}{\displaystyle 7}+b+\frac{\displaystyle 1}{\displaystyle 7}\\\\\frac{\displaystyle15}{\displaystyle 7} =b$

Therefore, the y-intercept of the line is $\frac{\displaystyle15}{\displaystyle 7}$ . Plug this back into $y=\frac{\displaystyle 1}{\displaystyle 7}x+b$ :

$y=\frac{\displaystyle 1}{\displaystyle 7}x+\frac{\displaystyle15}{\displaystyle 7}$

I hope this helps!

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3 years ago