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.
