Step-by-step explanation:
We will work to fill in the slope-intercept form of a line to get the answer to this. y = mx + b. The thing you need to understand first is how to get from one point to another on the line to determine the slope. Look to where the line goes through a corner of one of the squares on the graph. For example, locate these points to see what I mean: (-1, -2), (-2, -5), (1, 4), (2, 7). At each of those points, the line goes through perfectly right where the corners of the squares meet. If you understand this, then you are ready to write the equation of any line.
First locate the y-intercept. This is the point where the line goes through the y-axis. Our line goes through at a y value of +1. So our b value is +1. We will begin by filling that in first:
y = ___x + 1.
Now from that point, you can either go up and to the right to get to another point on the line, or you can go down and to the left. Let's do it both ways so you can see that regardless of which way you pick to go, you'll get the exact same equation every time.
I will go from the y-intercept to the point (1, 4). To get from the y-intercept, I have to go up 3 units til I'm even with the next point on the line, and then to the right 1. So my slope is +3/+1 which is 3.
If I want to go from the y-intercept to the point (-1, -2), I will go down 3 til I'm even with the point, then to the left 1. So my slope will be -3/-1 which is also a positive 3. Fill that in to the slope formula now:
y = 3x + 1, choice A.
