SOLUTION: use the point-slope form of the linear equation to find an equation of the line the given point. Then write the equation in standard form. Slope -5/8;through (2,5)

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: use the point-slope form of the linear equation to find an equation of the line the given point. Then write the equation in standard form. Slope -5/8;through (2,5)      Log On


   

Question 117148: use the point-slope form of the linear equation to find an equation of the line the given point. Then write the equation in standard form.
Slope -5/8;through (2,5)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

If you want to find the equation of line with a given a slope of -5%2F8 which goes through the point (2,5), you can simply use the point-slope formula to find the equation:


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

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

y-5=%28-5%2F8%29%28x-2%29 Plug in m=-5%2F8, x%5B1%5D=2, and y%5B1%5D=5 (these values are given)


y-5=%28-5%2F8%29x%2B%28-5%2F8%29%28-2%29 Distribute -5%2F8

y-5=%28-5%2F8%29x%2B5%2F4 Multiply -5%2F8 and -2 to get 5%2F4

y=%28-5%2F8%29x%2B5%2F4%2B5 Add 5 to both sides to isolate y

y=%28-5%2F8%29x%2B25%2F4 Combine like terms 5%2F4 and 5 to get 25%2F4 (note: if you need help with combining fractions, check out this solver)


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Answer:


So the equation of the line with a slope of -5%2F8 which goes through the point (2,5) is:

y=%28-5%2F8%29x%2B25%2F4 which is now in y=mx%2Bb form where the slope is m=-5%2F8 and the y-intercept is b=25%2F4

Notice if we graph the equation y=%28-5%2F8%29x%2B25%2F4 and plot the point (2,5), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-5%2F8%29x%2B25%2F4 through the point (2,5)
and we can see that the point lies on the line. Since we know the equation has a slope of -5%2F8 and goes through the point (2,5), this verifies our answer.