SOLUTION: Write and equation in slope-intercept form of the line that passes through the given points such as (12,-3),(-8,1)

Algebra ->  Linear-equations -> SOLUTION: Write and equation in slope-intercept form of the line that passes through the given points such as (12,-3),(-8,1)      Log On


   

Question 175465: Write and equation in slope-intercept form of the line that passes through the given points such as (12,-3),(-8,1)
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=%281--3%29%2F%28-8-12%29 Plug in y%5B2%5D=1, y%5B1%5D=-3, x%5B2%5D=-8, and x%5B1%5D=12


m=%284%29%2F%28-8-12%29 Subtract -3 from 1 to get 4


m=%284%29%2F%28-20%29 Subtract 12 from -8 to get -20


m=-1%2F5 Reduce


So the slope of the line that goes through the points and is m=-1%2F5


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--3=%28-1%2F5%29%28x-12%29 Plug in m=-1%2F5, x%5B1%5D=12, and y%5B1%5D=-3


y%2B3=%28-1%2F5%29%28x-12%29 Rewrite y--3 as y%2B3


y%2B3=%28-1%2F5%29x%2B%28-1%2F5%29%28-12%29 Distribute


y%2B3=%28-1%2F5%29x%2B12%2F5 Multiply


y=%28-1%2F5%29x%2B12%2F5-3 Subtract 3 from both sides.


y=%28-1%2F5%29x-3%2F5 Combine like terms. note: If you need help with fractions, check out this solver.


y=%28-1%2F5%29x-3%2F5 Simplify


So the equation that goes through the points and is y=%28-1%2F5%29x-3%2F5


Notice how the graph of y=%28-1%2F5%29x-3%2F5 goes through the points and . So this visually verifies our answer.
Graph of y=%28-1%2F5%29x-3%2F5 through the points and