SOLUTION: Write a slope-intercept equation for a line with the given circumstances. Passes through (-3,7) and (-1,-5)

Algebra ->  Coordinate-system -> SOLUTION: Write a slope-intercept equation for a line with the given circumstances. Passes through (-3,7) and (-1,-5)      Log On


   

Question 268904: Write a slope-intercept equation for a line with the given circumstances.
Passes through (-3,7) and (-1,-5)
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=-3 and y%5B1%5D=7.
Also, is the second point . So this means that x%5B2%5D=-1 and y%5B2%5D=-5.


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


m=%28-5-7%29%2F%28-1--3%29 Plug in y%5B2%5D=-5, y%5B1%5D=7, x%5B2%5D=-1, and x%5B1%5D=-3


m=%28-12%29%2F%28-1--3%29 Subtract 7 from -5 to get -12


m=%28-12%29%2F%282%29 Subtract -3 from -1 to get 2


m=-6 Reduce


So the slope of the line that goes through the points and is m=-6


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-7=-6%28x--3%29 Plug in m=-6, x%5B1%5D=-3, and y%5B1%5D=7


y-7=-6%28x%2B3%29 Rewrite x--3 as x%2B3


y-7=-6x%2B-6%283%29 Distribute


y-7=-6x-18 Multiply


y=-6x-18%2B7 Add 7 to both sides.


y=-6x-11 Combine like terms.


So the equation that goes through the points and is y=-6x-11


Notice how the graph of y=-6x-11 goes through the points and . So this visually verifies our answer.
Graph of y=-6x-11 through the points and