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#
