In this form for lines, m is the slope, and b is the y intercept. Hence, slope intercept. That means that in order to write it in this form, we need to know both the slope and y intercept. We'll start with the former.
Slope is defined as ride over run, or up over right (you know it's negative when it goes left). In order to calculate this, we can take two points that lie directly on a coordinate and put them into a fraction as rise/run.
We have;
(0,3) and (5,9)
As we can see, the difference between the two points is that (5,9) is 5 more to the right, and is 6 higher. We get 6/5. We can even see that in the coordinates, because they're written as (x, y). Additionally, you can use the slope given two points formula:
y2-y1/x2-x1 =
9-3/5-0 = 6/5
Notice how we get the same thing, because in both methods you're finding the difference between the two coordinates based off of rise/run. That's why it's y2 minus y1.
Now that we have our slope, we need the y intercept. The y intercept is simply where the line crosses the y axis. As we can see, it crosses at (0,3) - so the intercept is 3. Now we can create our equation
Slope = 6/5 Y intercept = 3
y = mx + b --> y = 6/5x + 3
Your answer is A, the first option. Hope this helps!
