Question

Which equation is graphed here?

Graph of a line containing the following points: (–4, 5), (–2, 2), (0, –1), and (2, –4).



y – 2 = (x + 4)



y – 4 = (x + 2)


y – 4 = (x + 2)

Answer 1

I would find the slope first. Take any two of the four points to find the slope of the line. So let's take the first two points. (-4,5) and (-2,2).

The slope is the rise over the run. So our slope looks like this:\[\frac{ 5-2 }{ -4+2 }=-\frac{ 3 }{ 2 }\]

Next I would find the b value. The b value is where the line crosses the y axis, so x would be equal to zero. Looking at the points you have been given I see one point (0,-1) where the x value is zero. So that's point we are after, and we see that the y value is -1. So the b value is -1.

Plunking the numbers for the slope and b value into the point slope form of a line (y=mx+b), where m is the slope and b is the point where the line crosses the y axis, we get this equation:\[y=-\frac{ 3 }{ 2 }-1\]
So we are looking for an answer we can rearrange to look like our equation.