SOLUTION: find the lope, the slope point form, slope intercept form, and standard form of the equation through the points (-5,6)(3,10) for slope intercept and standard form

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Question 167433: find the lope, the slope point form, slope intercept form, and standard form of the equation through the points (-5,6)(3,10) for slope intercept and standard form
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

y%2B9=%28-2%2F5%29%28x-3%29, EQN 1
It follows Point Slope Form Eqn: y=mx%2Bb
Continuing,
y=%28-2%2F5%29x%2B%286%2F5%29-9
y=%28-2%2F5%29x%2B%286-45%29%2F5
y=%28-2%2F5%29x%2B%28-39%2F5%29 ---> highlight%28slope=%28-2%2F5%29%29
In standard form:ax%2Bby=c, then EQN 1 becomes:
y%2B9=-2%2F5%28x-3%29 ---> y%2B%282%2F5%29x=%286%2F5%29-9
%282%2F5%29x%2By=%286-45%29%2F5=-39%2F5, multiply eqn by "5"
highlight%282x%2B5y=-39%29 --------> Standard Equation
.
Using Point-Slope Form for points (-5,6)(3,10):
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m=%2810-6%29%2F%283-%28-5%29%29=4%2F%283%2B5%29=4%2F8
highlight%28m=1%2F2%29, Slope
Thru points (-5,6), standard line eqn:
Via y=mx%2Bb
6=%281%2F2%29%28-5%29%2Bb
6%2B%285%2F2%29=b --> b=%2812%2B5%29%2F2 ---> b=17%2F2, y-intercept
Therefore it follows,
y=%281%2F2%29x%2B%2817%2F2%29 ---> %28-1%2F2%29x%2By=17%2F2, Multiply by "2" the eqn:
highlight%28-x%2B2y=17%29, STANDARD FORM
We'll see the graph:
--- See Green Line -x%2B2y=17 passes thru points (-5,6)(3,10)
Thank you,
Jojo