SOLUTION: 7. Write the equation of the line passing through each of the given pairs of points. Write your results in slope-intercept form, where possible (-5, 3) and (4, 1)

Algebra ->  Graphs -> SOLUTION: 7. Write the equation of the line passing through each of the given pairs of points. Write your results in slope-intercept form, where possible (-5, 3) and (4, 1)       Log On


   

Question 121215: 7. Write the equation of the line passing through each of the given pairs of points. Write your results in slope-intercept form, where possible
(-5, 3) and (4, 1)

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 (-5,3) and (4,1)

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 (-5,3) and is the second point (4,1))

m=%281-3%29%2F%284--5%29 Plug in y%5B2%5D=1,y%5B1%5D=3,x%5B2%5D=4,x%5B1%5D=-5 (these are the coordinates of given points)

m=+-2%2F9 Subtract the terms in the numerator 1-3 to get -2. Subtract the terms in the denominator 4--5 to get 9

So the slope is
m=-2%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 is one of the given points

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

y-3=%28-2%2F9%29%28x--5%29 Plug in m=-2%2F9, x%5B1%5D=-5, and y%5B1%5D=3 (these values are given)


y-3=%28-2%2F9%29%28x%2B5%29 Rewrite x--5 as x%2B5


y-3=%28-2%2F9%29x%2B%28-2%2F9%29%285%29 Distribute -2%2F9

y-3=%28-2%2F9%29x-10%2F9 Multiply -2%2F9 and 5 to get -10%2F9

y=%28-2%2F9%29x-10%2F9%2B3 Add 3 to both sides to isolate y

y=%28-2%2F9%29x%2B17%2F9 Combine like terms -10%2F9 and 3 to get 17%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 (-5,3) and (4,1) is:y=%28-2%2F9%29x%2B17%2F9

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-2%2F9 and the y-intercept is b=17%2F9

Notice if we graph the equation y=%28-2%2F9%29x%2B17%2F9 and plot the points (-5,3) and (4,1), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%28-2%2F9%29x%2B17%2F9 through the points (-5,3) and (4,1)

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