SOLUTION: Find an equation of the line described. Write the equation in the slope-intercept formif possible. through (6, -14) and (3, -2)?

Algebra ->  Linear-equations -> SOLUTION: Find an equation of the line described. Write the equation in the slope-intercept formif possible. through (6, -14) and (3, -2)?       Log On


   

Question 286207: Find an equation of the line described. Write the equation in the slope-intercept formif possible.
through (6, -14) and (3, -2)?



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


Note: is the first point . So this means that x%5B1%5D=6 and y%5B1%5D=-14.
Also, is the second point . So this means that x%5B2%5D=3 and y%5B2%5D=-2.


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


m=%28-2--14%29%2F%283-6%29 Plug in y%5B2%5D=-2, y%5B1%5D=-14, x%5B2%5D=3, and x%5B1%5D=6


m=%2812%29%2F%283-6%29 Subtract -14 from -2 to get 12


m=%2812%29%2F%28-3%29 Subtract 6 from 3 to get -3


m=-4 Reduce


So the slope of the line that goes through the points and is m=-4


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--14=-4%28x-6%29 Plug in m=-4, x%5B1%5D=6, and y%5B1%5D=-14


y%2B14=-4%28x-6%29 Rewrite y--14 as y%2B14


y%2B14=-4x%2B-4%28-6%29 Distribute


y%2B14=-4x%2B24 Multiply


y=-4x%2B24-14 Subtract 14 from both sides.


y=-4x%2B10 Combine like terms.


So the equation that goes through the points and is y=-4x%2B10