SOLUTION: Find the equation (in standard form) of the line through (1, –7) and (4, –1).

Algebra ->  Linear-equations -> SOLUTION: Find the equation (in standard form) of the line through (1, –7) and (4, –1).       Log On


   

Question 150555: Find the equation (in standard form) of the line through (1, –7) and (4, –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=%28-1--7%29%2F%284-1%29 Plug in y%5B2%5D=-1, y%5B1%5D=-7, x%5B2%5D=4, x%5B1%5D=1, ,


m=%286%29%2F%284-1%29 Subtract -7 from -1 to get 6


m=%286%29%2F%283%29 Subtract 1 from 4 to get 3


m=2 Reduce


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


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--7=2%28x-1%29 Plug in m=2, x%5B1%5D=1, and y%5B1%5D=-7


y%2B7=2%28x-1%29 Rewrite y--7 as y%2B7


y%2B7=2x%2B2%28-1%29 Distribute


y%2B7=2x-2 Multiply


y=2x-2-7 Subtract 7 from both sides.


y=2x-9 Combine like terms.


y=2x-9 Simplify. So the equation is now in slope-intercept form


y-2x=-9 Subtract 2x from both sides.


-2x%2By=-9 Rearrange the terms.


2x-y=9 Multiply everything by -1 to make the x coefficient positive (this step is optional).


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Answer:

So the equation that goes through the points and is


a) y=2x-9 which is slope-intercept form

or...

b) 2x-y=9 which is in standard form


Notice how the graph of y=2x-9 goes through the points and . So this visually verifies our answer.
Graph of y=2x-9 through the points and