Slope intercept form:
[tex]y = mx + b[/tex]
slope equation:
[tex]m = \frac{ y_{2} - y_{1} }{ x_{2} - x_{1} } [/tex]
Plug the points into the slope equation:
[tex]m = \frac{7 - 4}{3 - 7} [/tex]
[tex]m = - \frac{3}{4} [/tex]
Plug this back into the slope intercept formula:
[tex]y = mx + b[/tex]
[tex]y = - \frac{3}{4} x + b[/tex]
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.
[tex]7 = - \frac{3}{4} (3) + b \\ 7 = \frac{ - 9}{4} + b \\ 7 + \frac{9}{4} = b \\ \frac{28}{4} + \frac{9}{4} = b \\ \frac{37}{4} = b[/tex]
now plug this back into your slope intercept formula and you have your answer:
[tex]y = - ( \frac{3}{4} )x + \frac{37}{4} [/tex]
Try using the other point (7,4) to practice this technique. The answer for b will be the same for both. Hope this helped.
