SOLUTION: What is the equation for the line passing through the points (7,-8) and (-4, -4)?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What is the equation for the line passing through the points (7,-8) and (-4, -4)?      Log On


   

Question 76164This question is from textbook Algebra 1
: What is the equation for the line passing through the points (7,-8) and (-4, -4)? This question is from textbook Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (7,-8) and (-4,-4)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (7,-8) and (x%5B2%5D,y%5B2%5D) is the second point (-4,-4))


m=%28-4--8%29%2F%28-4-7%29 Plug in y%5B2%5D=-4,y%5B1%5D=-8,x%5B2%5D=-4,x%5B1%5D=7 (these are the coordinates of given points)


m=+4%2F-11 Subtract the terms in the numerator -4--8 to get 4. Subtract the terms in the denominator -4-7 to get -11




m=-4%2F11 Reduce



So the slope is

m=-4%2F11





------------------------------------------------


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 (x%5B1%5D,y%5B1%5D) is one of the given points


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


y--8=%28-4%2F11%29%28x-7%29 Plug in m=-4%2F11, x%5B1%5D=7, and y%5B1%5D=-8 (these values are given)



y%2B8=%28-4%2F11%29%28x-7%29 Rewrite y--8 as y%2B8



y%2B8=%28-4%2F11%29x%2B%28-4%2F11%29%28-7%29 Distribute -4%2F11


y%2B8=%28-4%2F11%29x%2B28%2F11 Multiply -4%2F11 and -7 to get 28%2F11

y=%28-4%2F11%29x%2B28%2F11-8 Subtract 8 from both sides to isolate y


y=%28-4%2F11%29x-60%2F11 Combine like terms 28%2F11 and -8 to get -60%2F11 (note: if you need help with combining fractions, check out this solver)



------------------------------------------------------------------------------------------------------------

Answer:



So the equation of the line which goes through the points (7,-8) and (-4,-4) is:y=%28-4%2F11%29x-60%2F11


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-4%2F11 and the y-intercept is b=-60%2F11


Notice if we graph the equation y=%28-4%2F11%29x-60%2F11 and plot the points (7,-8) and (-4,-4), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-4%2F11%29x-60%2F11 through the points (7,-8) and (-4,-4)


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



So in other words, the equation is:
y=%28-4%2F11%29x-60%2F11