SOLUTION: Find an equation of the line passing through the points (−15, −7) and (18, −7). Write your equation in standard form.

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Question 116141: Find an equation of the line passing through the points (−15, −7) and (18, −7). Write your equation in standard form.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First lets find the slope through the points (-15,-7) and (18,-7)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: is the first point (-15,-7) and is the second point (18,-7))

m=%28-7--7%29%2F%2818--15%29 Plug in y%5B2%5D=-7,y%5B1%5D=-7,x%5B2%5D=18,x%5B1%5D=-15 (these are the coordinates of given points)

m=+0%2F33 Subtract the terms in the numerator -7--7 to get 0. Subtract the terms in the denominator 18--15 to get 33


m=0 Reduce

So the slope is
m=0

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Now let's use the point-slope formula to find the equation of the line:



------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y--7=%280%29%28x--15%29 Plug in m=0, x%5B1%5D=-15, and y%5B1%5D=-7 (these values are given)


y%2B7=%280%29%28x--15%29 Rewrite y--7 as y%2B7


y%2B7=%280%29%28x%2B15%29 Rewrite x--15 as x%2B15


y%2B7=0x%2B%280%29%2815%29 Distribute 0

y%2B7=0x%2B0 Multiply 0 and 15 to get 0%2F0. Now reduce 0%2F0 to get 0

y=0x%2B0-7 Subtract 7 from both sides to isolate y

y=0x-7 Combine like terms 0 and -7 to get -7


y=-7 Remove the zero term
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Answer:


So the equation of the line which goes through the points (-15,-7) and (18,-7) is: y=-7

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=0 and the y-intercept is b=-7

Notice if we graph the equation y=-7 and plot the points (-15,-7) and (18,-7), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=-7 through the points (-15,-7) and (18,-7)

Notice how the two points lie on the line. This graphically verifies our answer.