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Find $y$ if the point $(-6,y)$ is on the line that passes through $(-1,7)$ and $(3,-2)$.
 Apr 11, 2023
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To find the equation of the line that passes through the points (-1,7) and (3,-2), we first need to determine the slope of the line:

slope = (change in y) / (change in x) slope = (7 - (-2)) / (-1 - (-3)) slope = 9 / 2

Now that we know the slope of the line, we can use the point-slope form of the equation of a line to find the equation of the line:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Using the point (-1,7), we get:

y - 7 = (9/2)(x - (-1)) y - 7 = (9/2)(x + 1) y - 7 = (9/2)x + 9/2 y = (9/2)x + 16/2 y = (9/2)x + 8

Now we need to find y when x = -6, since the point (-6,y) is on the line:

y = (9/2)(-6) + 8 y = -27 + 8 y = -19

Therefore, when the point (-6,y) is on the line that passes through (-1,7) and (3,-2), y is equal to -19.

 Apr 11, 2023

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