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Jane started jogging home from 5 miles away, at a rate of 2 mph. Which equation in slope-intercept form represents Jane's distance from home?
A. y = 2x − 5
B. y = −2x + 5
C. y = 2x + 5
D. y = −2x − 5

Respuesta :

danielmaduroh

B. y = −2x + 5

Explanation:

First of all, the slope-intercept form of the equation of a line is given by:

[tex]y=mx+b \\ \\ \\ Where: \\ \\ m:Slope \\ \\ b:y-intercept[/tex]

As the problem states, Jane started jogging home from 5 miles away, at a rate of 2 mph. In other words:

  • The starting point is 5 miles since Jane started jogging home from 5 miles away. So, starting the construction of our equation we would have:

[tex]y=5 \\ \\ y:Represents \ Janet's \ distance \ from \ home[/tex]

  • Jane is jogging at a rate of 2 mph. So this is the slope of the line we are constructing. But wait for a moment! The problem says that Jane started jogging home, that is, as time [tex]x[/tex] increases the distance from home must decrease. This is only valid if the rate of change is negative in other words, the slope must be -2. So:

[tex]y=-2x+5 \\ \\ y:Represents \ Janet's \ distance \ from \ home \\ \\ x:Represents \ time[/tex]

Finally, our correct option is:

B. y = −2x + 5

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