what is the equation of a line that passed through the point (-4,4) and has a slope of -2

Answer 1

Start with point-slope form (look for it in your text book)

(y - 4) = -2(x - (-4))

Answer 2

Let us start with what our target is. We are looking for an equation with the format y=mx+b

We are lucky, because we are told what m is as m represents the slope so let us update our target with this new piece of information! y=-2x+b

Now, we still need to figure out what b is because there are an infinite number of lines that have a slope of -2 so we need to figure the value of b out to determine the exact line that fits both of the conditions we were given. Luckily for us, we were given a point that the line goes through (-4,4), which means that when x=-4, y=4 so let us plug it into the equation and solve for b!

4 = -2(-4) + b

so 4 = 8 +b, and we subtract 8 from both sides to get -4 = b. Once we have both the slope and the value of b, we have the equation of the line so our final line equation will be y = -2x - 4