Eloise's car breaks down on a country road. She starts walking toward home at a rate of 1.5 miles an hour. After 2 hours, she is 10 miles from home.
Which equation in point-slope form models this situation?
y+10=1.5(x−2)
y+1.5=10(x−2)
y−10=2(x+1.5)
y−10=−1.5(x+2)
y−10=−1.5(x−2)
correct, if y is the distance from home.
I thincc its D?
ight Thanq
To determine which equation in point-slope form models the situation, we need to analyze the given information.
We know that Eloise starts walking toward home at a rate of 1.5 miles per hour and after 2 hours, she is 10 miles from home.
The point-slope form equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
In this case, y1 represents Eloise's distance from home after 2 hours, which is 10 miles. So we have y - 10.
The slope (m) represents Eloise's rate of walking, which is 1.5 miles per hour. Therefore, the slope is 1.5.
Now let's compare these values with the equations given:
1) y+10=1.5(x−2)
2) y+1.5=10(x−2)
The second equation does not match the point-slope form because the y-intercept is not 10.
3) y−10=2(x+1.5)
4) y−10=−1.5(x+2)
5) y−10=−1.5(x−2)
The correct equation that models this situation is y - 10 = -1.5(x - 2), which matches equation 5.