Question

Write an equation in slope-intercept form for the line that passes through (3, 7) and (7, 4) show work

Answer 1

Slope intercept form:


`y = mx + b`

slope equation:


`m = ( y_(2) - y_(1) )/( x_(2) - x_(1) )`

Plug the points into the slope equation:


`m = (7 - 4)/(3 - 7)`

`m = - (3)/(4)`

Plug this back into the slope intercept formula:


`y = mx + b`

`y = - (3)/(4) x + b`

Now plug in one of the points your given and we will solve for b:
I'll use (3, 7) but either one will work.


`7 = - (3)/(4) (3) + b \\ 7 = ( - 9)/(4) + b \\ 7 + (9)/(4) = b \\ (28)/(4) + (9)/(4) = b \\ (37)/(4) = b`

now plug this back into your slope intercept formula and you have your answer:


`y = - ( (3)/(4) )x + (37)/(4)`

Try using the other point (7,4) to practice this technique. The answer for b will be the same for both. Hope this helped.