SOLUTION: Give the slope-intercept form of the equation for the line on which these two points lie: (4, -2) and (3, 8)

Algebra ->  Graphs -> SOLUTION: Give the slope-intercept form of the equation for the line on which these two points lie: (4, -2) and (3, 8)      Log On


   

Question 275934: Give the slope-intercept form of the equation for the line on which these two points lie: (4, -2) and (3, 8)
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=4 and y%5B1%5D=-2.
Also, is the second point . So this means that x%5B2%5D=3 and y%5B2%5D=8.


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


m=%288--2%29%2F%283-4%29 Plug in y%5B2%5D=8, y%5B1%5D=-2, x%5B2%5D=3, and x%5B1%5D=4


m=%2810%29%2F%283-4%29 Subtract -2 from 8 to get 10


m=%2810%29%2F%28-1%29 Subtract 4 from 3 to get -1


m=-10 Reduce


So the slope of the line that goes through the points and is m=-10


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--2=-10%28x-4%29 Plug in m=-10, x%5B1%5D=4, and y%5B1%5D=-2


y%2B2=-10%28x-4%29 Rewrite y--2 as y%2B2


y%2B2=-10x%2B-10%28-4%29 Distribute


y%2B2=-10x%2B40 Multiply


y=-10x%2B40-2 Subtract 2 from both sides.


y=-10x%2B38 Combine like terms.


So the equation that goes through the points and is y=-10x%2B38