What is the equation of a line that goes through (2,2) and (3,6)?

1 Answer

y=4x6

Explanation:

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=y2y1x2x1

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=6232=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=4x6