SOLUTION: Please help... Write the equation of line passing through each of the given pairs of points. Write your result in slope-intercept form. 1) (0,5),M= -3/5 2) (-1,3) and (4, -2)

Algebra ->  Linear-equations -> SOLUTION: Please help... Write the equation of line passing through each of the given pairs of points. Write your result in slope-intercept form. 1) (0,5),M= -3/5 2) (-1,3) and (4, -2)       Log On


   

Question 120424: Please help...
Write the equation of line passing through each of the given pairs of points. Write your result in slope-intercept form.
1) (0,5),M= -3/5
2) (-1,3) and (4, -2)
3) (2,-3) and (2,4)
Find the slope of any line perpendicular to the line through points (0,5) and (-3,-4).

Thank you for your help on this...
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1


If you want to find the equation of line with a given a slope of -3%2F5 which goes through the point (0,5), 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=%28-3%2F5%29%28x-0%29 Plug in m=-3%2F5, x%5B1%5D=0, and y%5B1%5D=5 (these values are given)


y-5=%28-3%2F5%29x%2B%28-3%2F5%29%28-0%29 Distribute -3%2F5

y-5=%28-3%2F5%29x%2B0 Multiply -3%2F5 and -0 to get 0

y=%28-3%2F5%29x%2B0%2B5 Add 5 to both sides to isolate y

y=%28-3%2F5%29x%2B5 Combine like terms 0 and 5 to get 5
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Answer:


So the equation of the line with a slope of -3%2F5 which goes through the point (0,5) is:

y=%28-3%2F5%29x%2B5 which is now in y=mx%2Bb form where the slope is m=-3%2F5 and the y-intercept is b=5

Notice if we graph the equation y=%28-3%2F5%29x%2B5 and plot the point (0,5), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-3%2F5%29x%2B5 through the point (0,5)
and we can see that the point lies on the line. Since we know the equation has a slope of -3%2F5 and goes through the point (0,5), this verifies our answer.





#2

First lets find the slope through the points (-1,3) and (4,-2)

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 (-1,3) and is the second point (4,-2))

m=%28-2-3%29%2F%284--1%29 Plug in y%5B2%5D=-2,y%5B1%5D=3,x%5B2%5D=4,x%5B1%5D=-1 (these are the coordinates of given points)

m=+-5%2F5 Subtract the terms in the numerator -2-3 to get -5. Subtract the terms in the denominator 4--1 to get 5


m=-1 Reduce

So the slope is
m=-1

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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=%28-1%29%28x--1%29 Plug in m=-1, x%5B1%5D=-1, and y%5B1%5D=3 (these values are given)


y-3=%28-1%29%28x%2B1%29 Rewrite x--1 as x%2B1


y-3=-x%2B%28-1%29%281%29 Distribute -1

y-3=-x-1 Multiply -1 and 1 to get -1

y=-x-1%2B3 Add 3 to both sides to isolate y

y=-x%2B2 Combine like terms -1 and 3 to get 2
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Answer:


So the equation of the line which goes through the points (-1,3) and (4,-2) is:y=-x%2B2

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1 and the y-intercept is b=2

Notice if we graph the equation y=-x%2B2 and plot the points (-1,3) and (4,-2), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=-x%2B2 through the points (-1,3) and (4,-2)

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





#3

First lets find the slope through the points (2,-3) 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 (2,-3) and is the second point (2,4))

m=%284--3%29%2F%282-2%29 Plug in y%5B2%5D=4,y%5B1%5D=-3,x%5B2%5D=2,x%5B1%5D=2 (these are the coordinates of given points)

m=+7%2F0 Subtract the terms in the numerator 4--3 to get 7. Subtract the terms in the denominator 2-2 to get 0


Since the denominator is zero, the slope is undefined (remember you cannot divide by zero). So we cannot use the slope intercept form to write an equation. So we can only say that the equation is a vertical line through x=2, which means the equation is x=2 (notice this is not in slope-intercept form)


So the equation x=2 looks like this:
Graph of x=2 through the points (2,-3) and (2,4)







First find the slope through the points (0,5) and (-3,-4).


Solved by pluggable solver: Finding the slope


Slope of the line through the points (0, 5) and (-3, -4)



Answer: Slope is m+=+3


If you're given a slope of m=3, you can find the perpendicular slope by negating and inverting the given slope.

In other words, use this formula to find the perpendicular slope:
m%5Bp%5D=-1%2Fm where m is the given slope and m%5Bp%5D is the perpendicular slope

m%5Bp%5D=-1%2F%283%2F1%29 plug in m=3%2F1 (note: remember 3 really looks like 3%2F1)

m%5Bp%5D=%28-1%2F1%29%281%2F3%29 Flip the second fraction and multiply

m%5Bp%5D=-1%2F3 Multiply

So the perpendicular slope is -1%2F3