Question

Find the equation of the line.

Answer 1

Hey there! I'm happy to help!

The slope-intercept equation for a line is y=mx+b. It looks like we need to find m and b, where m is the slope, which is the steepness of the line, and b is the y-intercept, where the line hits the y-axis.

Well, from looking at the graph. we immediately see that the line hits the y-axis at (0,4), so this means that the y-intercept, or b, is four.

The slope is pretty easy to find as well. The first thing we need to do is find two points on the line. Well, we have already found one point on the line: (0,4). One other nice point I see is (3,6). Let's use these two to find the slope.

The find the slope, you divide the vertical distance between the two points by the horizontal distance between them.

We see that (3,6) is two squares higher than (0,4). So, our dividend is 2.

Horizontally, we also see that (3,6) is three squares to the right of (0,4). So, our divisor is 3.

This means that our slope, or m is 2/3. This makes sense because for every 1 square to the right the line goes, it goes up 2/3.

Therefore, your equation is y=2/3+4.

Have a wonderful day!