SOLUTION: Write an equation in slope-intercept form for a line that passes through (7,-3) and has a y-intercept of 2

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Question 176441: Write an equation in slope-intercept form for a line that passes through (7,-3) and has a y-intercept of 2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: a y-intercept of 2 means that the point (0,2) is on the line


So let's find the equation of the line through (7,-3) and (0,2)




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=%282--3%29%2F%280-7%29 Plug in y%5B2%5D=2, y%5B1%5D=-3, x%5B2%5D=0, and x%5B1%5D=7


m=%285%29%2F%280-7%29 Subtract -3 from 2 to get 5


m=%285%29%2F%28-7%29 Subtract 7 from 0 to get -7


m=-5%2F7 Reduce


So the slope of the line that goes through the points and is m=-5%2F7


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--3=%28-5%2F7%29%28x-7%29 Plug in m=-5%2F7, x%5B1%5D=7, and y%5B1%5D=-3


y%2B3=%28-5%2F7%29%28x-7%29 Rewrite y--3 as y%2B3


y%2B3=%28-5%2F7%29x%2B%28-5%2F7%29%28-7%29 Distribute


y%2B3=%28-5%2F7%29x%2B5 Multiply


y=%28-5%2F7%29x%2B5-3 Subtract 3 from both sides.


y=%28-5%2F7%29x%2B2 Combine like terms.


y=%28-5%2F7%29x%2B2 Simplify


So the equation that goes through the points and is y=%28-5%2F7%29x%2B2


Notice how the graph of y=%28-5%2F7%29x%2B2 goes through the points and . So this visually verifies our answer.
Graph of y=%28-5%2F7%29x%2B2 through the points and