SOLUTION: Hi! This is another (Write an equation thing), basically is says : Write an equation for the line going through the points (3,2) and (-2,4). Please and Thank You=)

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Question 130381This question is from textbook algebra
: Hi! This is another (Write an equation thing), basically is says : Write an equation for the line going through the points (3,2) and (-2,4).
Please and Thank You=) This question is from textbook algebra

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 (3,2) and (-2,4)

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 (3,2) and is the second point (-2,4))

m=%284-2%29%2F%28-2-3%29 Plug in y%5B2%5D=4,y%5B1%5D=2,x%5B2%5D=-2,x%5B1%5D=3 (these are the coordinates of given points)

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


m=-2%2F5 Reduce

So the slope is
m=-2%2F5

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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-2=%28-2%2F5%29%28x-3%29 Plug in m=-2%2F5, x%5B1%5D=3, and y%5B1%5D=2 (these values are given)


y-2=%28-2%2F5%29x%2B%28-2%2F5%29%28-3%29 Distribute -2%2F5

y-2=%28-2%2F5%29x%2B6%2F5 Multiply -2%2F5 and -3 to get 6%2F5

y=%28-2%2F5%29x%2B6%2F5%2B2 Add 2 to both sides to isolate y

y=%28-2%2F5%29x%2B16%2F5 Combine like terms 6%2F5 and 2 to get 16%2F5 (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 (3,2) and (-2,4) is:y=%28-2%2F5%29x%2B16%2F5

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-2%2F5 and the y-intercept is b=16%2F5

Notice if we graph the equation y=%28-2%2F5%29x%2B16%2F5 and plot the points (3,2) and (-2,4), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%28-2%2F5%29x%2B16%2F5 through the points (3,2) and (-2,4)

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