Find an equation of the line containing the given pair of points (4,5) and (12,12)

Question

I am really stuck, please help me solve this problem

Answer 1

Hi Suzanne.

 

To right the equation of a line, you need a point and the slope of the line.

 

The slope is (y2-y1)/(x2-x1).

 

or  slope = (12-5)/(12-4)  = 7/8

 

Now choose your favorite point.  I will use (4,5)

 

y=mx+b   

 

Plug in your x (4), your y (5) and your slope (m=7/8) and solve for b.   

 

5=(7/8)(4)+b = (7/2) + b

 

So 5-(7/2) =b  or b=3/2 or 1.5

 

Now, the equation of the line KEEPS x and y in it, and just replace the slope (m) and the y-intercept (b)

 

y=(7/8)x+1.5

 

And you can check:  Plug in x=12 and see if you get y=12.  Plug in x=4 and see if you get y=5.