Match the graph with the correct equation

y + 2 = -(x - 4)

Explanation:

The slope of this line is -1 because each time we move down 2 units, we move to the right 2 units. So slope = rise/run = -2/2 = -1

The slope formula says the same thing more or less. Let's pick the two points (0,2) and (2,0) to find the slope through them

m = (y2-y1)/(x2 - x1)

m = (0-2)/(2-0)

m = -2/2

m = -1

Using that slope and a point on the line, we can form the equation. We can pick any point really as long as it's on the line. However, to have it match with the answer choices, we'll have to pick the point (4,-2)

Turn to point slope form

y - y1 = m(x - x1)

y - y1 = -1(x - x1) ... plug in the slope

y  - (-2) = -(x - 4) ... plug in the point (x1,y1) = (4, -2)

y + 2 = -(x - 4)