SOLUTION: how do i write an equation in slope-intercept form for the line that satisfies each set of conditions Example The slope -2/3, passes through (6,-8)

Algebra ->  Linear-equations -> SOLUTION: how do i write an equation in slope-intercept form for the line that satisfies each set of conditions Example The slope -2/3, passes through (6,-8)      Log On


   

Question 215352: how do i write an equation in slope-intercept form for the line that satisfies each set of conditions Example The slope -2/3, passes through (6,-8)
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 -2%2F3 which goes through the point (6,-8), 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--8=%28-2%2F3%29%28x-6%29 Plug in m=-2%2F3, x%5B1%5D=6, and y%5B1%5D=-8 (these values are given)


y%2B8=%28-2%2F3%29%28x-6%29 Rewrite y--8 as y%2B8


y%2B8=%28-2%2F3%29x%2B%28-2%2F3%29%28-6%29 Distribute -2%2F3

y%2B8=%28-2%2F3%29x%2B4 Multiply -2%2F3 and -6 to get 4

y=%28-2%2F3%29x%2B4-8 Subtract 8 from both sides to isolate y

y=%28-2%2F3%29x-4 Combine like terms 4 and -8 to get -4
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Answer:


So the equation of the line with a slope of -2%2F3 which goes through the point (6,-8) is:

y=%28-2%2F3%29x-4 which is now in y=mx%2Bb form where the slope is m=-2%2F3 and the y-intercept is b=-4

Notice if we graph the equation y=%28-2%2F3%29x-4 and plot the point (6,-8), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-2%2F3%29x-4 through the point (6,-8)
and we can see that the point lies on the line. Since we know the equation has a slope of -2%2F3 and goes through the point (6,-8), this verifies our answer.