SOLUTION: What is the equation of the solution in point-slope form and slope-intercept form? Passing through (-4,-2) and (1,3)

Algebra ->  Linear-equations -> SOLUTION: What is the equation of the solution in point-slope form and slope-intercept form? Passing through (-4,-2) and (1,3)      Log On


   

Question 613005: What is the equation of the solution in point-slope form and slope-intercept form? Passing through (-4,-2) and (1,3)
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


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=1 and y%5B2%5D=3.


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%281--4%29 Plug in y%5B2%5D=3, y%5B1%5D=-2, x%5B2%5D=1, and x%5B1%5D=-4


m=%285%29%2F%281--4%29 Subtract -2 from 3 to get 5


m=%285%29%2F%285%29 Subtract -4 from 1 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--2=1%28x--4%29 Plug in m=1, x%5B1%5D=-4, and y%5B1%5D=-2


y--2=1%28x%2B4%29 Rewrite x--4 as x%2B4


y%2B2=1%28x%2B4%29 Rewrite y--2 as y%2B2


y%2B2=1x%2B1%284%29 Distribute


y%2B2=1x%2B4 Multiply


y=1x%2B4-2 Subtract 2 from both sides.


y=1x%2B2 Combine like terms.


y=x%2B2 Simplify


So the equation that goes through the points and is y=x%2B2


Notice how the graph of y=x%2B2 goes through the points and . So this visually verifies our answer.
Graph of y=x%2B2 through the points and