SOLUTION: Write the slope-intercept form of the equation of the line shown in the graph. Please show all of your work. (-6, -2) (4, 3)

Algebra ->  Linear-equations -> SOLUTION: Write the slope-intercept form of the equation of the line shown in the graph. Please show all of your work. (-6, -2) (4, 3)      Log On


   

Question 368566: Write the slope-intercept form of the equation of the line shown in the graph. Please show all of your work.

(-6, -2) (4, 3)
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=%283--2%29%2F%284--6%29 Plug in y%5B2%5D=3, y%5B1%5D=-2, x%5B2%5D=4, and x%5B1%5D=-6


m=%285%29%2F%284--6%29 Subtract -2 from 3 to get 5


m=%285%29%2F%2810%29 Subtract -6 from 4 to get 10


m=1%2F2 Reduce


So the slope of the line that goes through the points and is m=1%2F2


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=%281%2F2%29%28x--6%29 Plug in m=1%2F2, x%5B1%5D=-6, and y%5B1%5D=-2


y--2=%281%2F2%29%28x%2B6%29 Rewrite x--6 as x%2B6


y%2B2=%281%2F2%29%28x%2B6%29 Rewrite y--2 as y%2B2


y%2B2=%281%2F2%29x%2B%281%2F2%29%286%29 Distribute


y%2B2=%281%2F2%29x%2B3 Multiply


y=%281%2F2%29x%2B3-2 Subtract 2 from both sides.


y=%281%2F2%29x%2B1 Combine like terms.


So the equation that goes through the points and is y=%281%2F2%29x%2B1


Notice how the graph of y=%281%2F2%29x%2B1 goes through the points and . So this visually verifies our answer.
Graph of y=%281%2F2%29x%2B1 through the points and