SOLUTION: Write the slope-intercept form of the equation of the line through the given points. through: (-4,-2) and (5,2)

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Question 1021005: Write the slope-intercept form of the equation of the line through the given points.
through: (-4,-2) and (5,2)
Answer by MathLover1(20850) 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 (-4,-2) and (5,2)


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 (-4,-2) and (x%5B2%5D,y%5B2%5D) is the second point (5,2))


m=%282--2%29%2F%285--4%29 Plug in y%5B2%5D=2,y%5B1%5D=-2,x%5B2%5D=5,x%5B1%5D=-4 (these are the coordinates of given points)


m=+4%2F9 Subtract the terms in the numerator 2--2 to get 4. Subtract the terms in the denominator 5--4 to get 9



So the slope is

m=4%2F9





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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 (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--2=%284%2F9%29%28x--4%29 Plug in m=4%2F9, x%5B1%5D=-4, and y%5B1%5D=-2 (these values are given)



y%2B2=%284%2F9%29%28x--4%29 Rewrite y--2 as y%2B2



y%2B2=%284%2F9%29%28x%2B4%29 Rewrite x--4 as x%2B4



y%2B2=%284%2F9%29x%2B%284%2F9%29%284%29 Distribute 4%2F9


y%2B2=%284%2F9%29x%2B16%2F9 Multiply 4%2F9 and 4 to get 16%2F9

y=%284%2F9%29x%2B16%2F9-2 Subtract 2 from both sides to isolate y


y=%284%2F9%29x-2%2F9 Combine like terms 16%2F9 and -2 to get -2%2F9 (note: if you need help with combining fractions, check out this solver)



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Answer:



So the equation of the line which goes through the points (-4,-2) and (5,2) is:y=%284%2F9%29x-2%2F9


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=4%2F9 and the y-intercept is b=-2%2F9


Notice if we graph the equation y=%284%2F9%29x-2%2F9 and plot the points (-4,-2) and (5,2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%284%2F9%29x-2%2F9 through the points (-4,-2) and (5,2)


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