The equation of the line through the point (-4, 7) and with a slope of -5/2 is y = -5/2x - 3
The equation of a line in slope intercept form is expressed as:
[tex]y-y_0 = m(x-x_0)[/tex]
m is the slope
(x0, y0) is the point on the line.
Given the following parameters:
m = -5/2 and (x0, y0) =(-4, 7)
Substitute the given coordinates into the formula above;
y - 7 = -5/2(x + 4)
2(y-7) = -5(x+4)
2y-14 = -5x - 20
2y = -5x - 20 + 14
2y = -5x - 6
y = -5/2x - 3
Hence the equation of the line through the point (-4, 7) and with a slope of -5/2 is y = -5/2x - 3
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