Question

What is the equation in slope intercept form (y=Mx+b) of the line that passes through the point (7, -3) and has a slope of -5?

Answer 1

Answer:  y = -5x+32

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Work Shown:

You can use point slope form by plugging in m = -5 and $(x_1, y_1) = (7,-3)$

So,

$y - y_1 = m(x - x_1)\\\\y - (-3) = -5(x - 7)\\\\y + 3 = -5(x - 7)\\\\y + 3 = -5x + 35\\\\y + 3-3 = -5x + 35-3 \text{ subtract 3 from both sides} \\\\y = -5x + 32$

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Or you could use y = mx+b to solve for the value of b

Plug in m = -5, and (x,y) = (7,-3)

$y = mx+b\\\\-3 = (-5)(7)+b\\\\-3 = -35+b\\\\-3+35 = -35+b+35\\\\32 = b\\\\b = 32$

Since m = -5 and b = 32, we know that y = -5x+32 is the equation of the line.