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)

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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)   (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 which goes through the point (,), you can simply use the point-slope formula to find the equation:


---Point-Slope Formula---
where is the slope, and is the given point

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

Plug in , , and (these values are given)


Distribute

Multiply and to get

Add 5 to both sides to isolate y

Combine like terms and to get
------------------------------------------------------------------------------------------------------------
Answer:


So the equation of the line with a slope of which goes through the point (,) is:

which is now in form where the slope is and the y-intercept is

Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver)

Graph of through the point (,)
and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.





#2

First lets find the slope through the points (,) and (,)

Start with the slope formula (note: is the first point (,) and is the second point (,))

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get


Reduce

So the slope is


------------------------------------------------


Now let's use the point-slope formula to find the equation of the line:



------Point-Slope Formula------
where is the slope, and is one of the given points

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

Plug in , , and (these values are given)


Rewrite as


Distribute

Multiply and to get

Add to both sides to isolate y

Combine like terms and to get
------------------------------------------------------------------------------------------------------------
Answer:


So the equation of the line which goes through the points (,) and (,) is:

The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is

Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver)

Graph of through the points (,) and (,)

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





#3

First lets find the slope through the points (,) and (,)

Start with the slope formula (note: is the first point (,) and is the second point (,))

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get


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 , which means the equation is (notice this is not in slope-intercept form)


So the equation looks like this:
Graph of through the points (,) and (,)







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


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

In other words, use this formula to find the perpendicular slope:
where m is the given slope and is the perpendicular slope

plug in (note: remember really looks like )

Flip the second fraction and multiply

Multiply

So the perpendicular slope is



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