SOLUTION: Hi, My question is how do you wrute and graph the equation of the line that goes through (0,0) and (-3,9). Also how do i find the slope a line that passes through the points (4,2

Algebra ->  Linear-equations -> SOLUTION: Hi, My question is how do you wrute and graph the equation of the line that goes through (0,0) and (-3,9). Also how do i find the slope a line that passes through the points (4,2      Log On


   

Question 555463: Hi,
My question is how do you wrute and graph the equation of the line that goes through (0,0) and (-3,9). Also how do i find the slope a line that passes through the points (4,2) and (-6,-3). But I need the answer ny tomorrow morning though.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1



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=0 and y%5B1%5D=0.
Also, is the second point . So this means that x%5B2%5D=-3 and y%5B2%5D=9.


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


m=%289-0%29%2F%28-3-0%29 Plug in y%5B2%5D=9, y%5B1%5D=0, x%5B2%5D=-3, and x%5B1%5D=0


m=%289%29%2F%28-3-0%29 Subtract 0 from 9 to get 9


m=%289%29%2F%28-3%29 Subtract 0 from -3 to get -3


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-0=-3%28x-0%29 Plug in m=-3, x%5B1%5D=0, and y%5B1%5D=0


y-0=-3x%2B-3%28-0%29 Distribute


y-0=-3x%2B0 Multiply


y=-3x%2B0%2B0 Add 0 to both sides.


y=-3x%2B0 Combine like terms.


y=-3x Remove the trailing zero



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


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

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# 2

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=-6 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=%28-3-2%29%2F%28-6-4%29 Plug in y%5B2%5D=-3, y%5B1%5D=2, x%5B2%5D=-6, and x%5B1%5D=4


m=%28-5%29%2F%28-6-4%29 Subtract 2 from -3 to get -5


m=%28-5%29%2F%28-10%29 Subtract 4 from -6 to get -10


m=1%2F2 Reduce


So the slope of the line that goes through the points and is m=1%2F2

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Jim