Step 1: You have two points in your question: (2,2) and (3,6). What you need to do, is use the slope formula. The slope formula is
slope=m=y2−y1x2−x1
Step 2: So let's look at the first point in the question. (2,2) is (x1,y1. That means that 2=x1 and 2=y1. Now, let's do the same thing with the Second point (3,6). Here 3=x2 and 6=y2.
Step 3: Let's plug those numbers into our equation. So we have
m=6−23−2=41
That gives us an answer of 4! And the slope is represented by the letter m.
Step 4: Now let's use our equation of a line formula. That slope-intercept equation of a line is
y=mx+b
Step 5: Plug in one of the points: either (2,2) or (3,6) into y=mx+b. Thus, you have
6=m3+b
Or you have
2=m2+b
Step 6: You have 6=m3+b OR you have 2=m2+b. We also found our m earlier in step 3. So if you plug in the m, you have
6=4(3)+b or 2=4(2)+b
Step 7: Multiply the 4 and 3 together. That gives you 12. So you have
6=12+b
Subtract the 12 from both sides and you now have
−6=b
OR
Multiply 4 and 2 together. That gives you 8. So you have
2=8+b
Subtract 8 from both sides and you now have
−6=b
Step 8: So you have found b and m! That was the goal! So your equation of a line that goes through (2,2) and (3,6) is
y=4x−6