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

1 Answer
Mar 6, 2018

y= 4x-6

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 = (y_2-y_1)/(x_2-x_1)

Step 2: So let's look at the first point in the question. (2,2) is (x_1,y_1. That means that 2= x_1 and 2= y_1. Now, let's do the same thing with the Second point (3,6). Here 3= x_2 and 6= y_2.

Step 3: Let's plug those numbers into our equation. So we have

m = (6-2)/(3-2) = 4/1

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