what is the equation of a line with a slope of −4 and a point (−2, 5) on the line? express the equation in the form of y=mx+b where m is the slope and b is the y-intercept.

We will use the slope-intercept form, y = mx + b, that the problem asks for.

y = mx + b

m = slope
We are given slope = -4, so we have m = -4, and we can already put that slope in the equation for m.

y = -4x + b

Now we need to find b, the y-intercept.
We are given point (-2, 5), so we have an x value of -2 and a y value of -5.
We plug in -2 for x and 5 for y in y = -4x + b, and we solve fro b, the y-intercept.

y = -4x + b

5 = -4(-2) + b

5 = 8 + b

b = -3

Now that we have b = -3, we replace b with -3.

y = -4x + b

y = -4x - 3

y = -4x - 3