SOLUTION: Write the equation in slope-intercept form of the line that contains the points (4, -7) and (0, 5).

Algebra ->  Linear-equations -> SOLUTION: Write the equation in slope-intercept form of the line that contains the points (4, -7) and (0, 5).       Log On


   

Question 554308: Write the equation in slope-intercept form of the line that contains the points (4, -7) and (0, 5).
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=-7.
Also, is the second point . So this means that x%5B2%5D=0 and y%5B2%5D=5.


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


m=%285--7%29%2F%280-4%29 Plug in y%5B2%5D=5, y%5B1%5D=-7, x%5B2%5D=0, and x%5B1%5D=4


m=%2812%29%2F%280-4%29 Subtract -7 from 5 to get 12


m=%2812%29%2F%28-4%29 Subtract 4 from 0 to get -4


m=-3 Reduce


So the slope of the line that goes through the points and is m=-3


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=-3%28x-4%29 Plug in m=-3, x%5B1%5D=4, and y%5B1%5D=-7


y%2B7=-3%28x-4%29 Rewrite y--7 as y%2B7


y%2B7=-3x%2B-3%28-4%29 Distribute


y%2B7=-3x%2B12 Multiply


y=-3x%2B12-7 Subtract 7 from both sides.


y=-3x%2B5 Combine like terms.


y=-3x%2B5 Simplify


So the equation that goes through the points and is y=-3x%2B5


Notice how the graph of y=-3x%2B5 goes through the points and . So this visually verifies our answer.
Graph of y=-3x%2B5 through the points and


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Jim