SOLUTION: Find the equation of the line that passes throught these two points (-12,-15) and (-16,-6). Write in Standard general form.

Algebra ->  Linear-equations -> SOLUTION: Find the equation of the line that passes throught these two points (-12,-15) and (-16,-6). Write in Standard general form.      Log On


   

Question 150633: Find the equation of the line that passes throught these two points (-12,-15) and (-16,-6). Write in Standard general form.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28-6--15%29%2F%28-16--12%29 Plug in y%5B2%5D=-6, y%5B1%5D=-15, x%5B2%5D=-16, x%5B1%5D=-12, ,


m=%289%29%2F%28-16--12%29 Subtract -15 from -6 to get 9


m=%289%29%2F%28-4%29 Subtract -12 from -16 to get -4


m=-9%2F4 Reduce


So the slope of the line that goes through the points and is m=-9%2F4


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--15=%28-9%2F4%29%28x--12%29 Plug in m=-9%2F4, x%5B1%5D=-12, and y%5B1%5D=-15


y--15=%28-9%2F4%29%28x%2B12%29 Rewrite x--12 as x%2B12


y%2B15=%28-9%2F4%29%28x%2B12%29 Rewrite y--15 as y%2B15


y%2B15=%28-9%2F4%29x%2B%28-9%2F4%29%2812%29 Distribute


y%2B15=%28-9%2F4%29x-27 Multiply


y=%28-9%2F4%29x-27-15 Subtract 15 from both sides.


y=%28-9%2F4%29x-42 Combine like terms.


y=%28-9%2F4%29x-42 Simplify


4y=4%28%28-9%2Fcross%284%29%29x-42%29 Multiply both sides by 4 to clear the fraction.


4y=-9x-168 Distribute and multiply.


4y%2B9x=-168 Add 9x to both sides.


9x%2B4y=-168 Rearrange the terms


So the equation in standard form that goes through the points and is 9x%2B4y=-168