SOLUTION: write an equation in point slope form and standard form of the line that passes through the given points: (-5,2),(-4,3)

Algebra ->  Linear-equations -> SOLUTION: write an equation in point slope form and standard form of the line that passes through the given points: (-5,2),(-4,3)      Log On


   

Question 178994This question is from textbook
: write an equation in point slope form and standard form of the line that passes through the given points: (-5,2),(-4,3) This question is from textbook

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 and is the second point .


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%28-4--5%29 Plug in y%5B2%5D=3, y%5B1%5D=2, x%5B2%5D=-4, and x%5B1%5D=-5


m=%281%29%2F%28-4--5%29 Subtract 2 from 3 to get 1


m=%281%29%2F%281%29 Subtract -5 from -4 to get 1


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


y-2=1%28x%2B5%29 Rewrite x--5 as x%2B5


y-2=1x%2B1%285%29 Distribute


y-2=1x%2B5 Multiply


y=1x%2B5%2B2 Add 2 to both sides.


y=1x%2B7 Combine like terms.


y=x%2B7 Simplify


So the equation in slope intercept form that goes through the points and is y=x%2B7


Now let's convert y=x%2B7 to standard form:


y=x%2B7 Start with the given equation.


y-x=7 Subtract x from both sides.


-x%2By=7 Rearrange the terms.


x-y=-7 Multiply EVERY term by -1 to make the x coefficient positive.


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Answer:

So the slope intercept equation is y=x%2B7 and the standard equation is x-y=-7