SOLUTION: 16. Write the slope-intercept equation for the line that passes through (-2, 7) and (-7, 12). Please show all of your work.

Algebra ->  Linear-equations -> SOLUTION: 16. Write the slope-intercept equation for the line that passes through (-2, 7) and (-7, 12). Please show all of your work.       Log On


   

Question 487054: 16. Write the slope-intercept equation for the line that passes through (-2, 7) and (-7, 12). Please show all of your work.
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=-2 and y%5B1%5D=7.
Also, is the second point . So this means that x%5B2%5D=-7 and y%5B2%5D=12.


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


m=%2812-7%29%2F%28-7--2%29 Plug in y%5B2%5D=12, y%5B1%5D=7, x%5B2%5D=-7, and x%5B1%5D=-2


m=%285%29%2F%28-7--2%29 Subtract 7 from 12 to get 5


m=%285%29%2F%28-5%29 Subtract -2 from -7 to get -5


m=-1 Reduce


So the slope of the line that goes through the points and is m=-1


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


y-7=-1%28x%2B2%29 Rewrite x--2 as x%2B2


y-7=-1x%2B-1%282%29 Distribute


y-7=-1x-2 Multiply


y=-1x-2%2B7 Add 7 to both sides.


y=-1x%2B5 Combine like terms.


y=-x%2B5 Simplify


So the equation that goes through the points and is y=-x%2B5