SOLUTION: These 3 problems do not come from a book but I really need help with them! If you can solve them as soon as possible, I would greatly appreciate it. Here they are: #1: Write t

Question 98453: These 3 problems do not come from a book but I really need help with them!
If you can solve them as soon as possible, I would greatly appreciate it.
Here they are:
#1:
Write the equation of the line passing through the points listed below. Write the final answer in the slope-intercept form y = mx + b. If the slope (m) or the y-intercept (b) are not integers, fractions must be used.
(-1, 8); (9, 2)

#2:
A line passes through the origin and the point (-6, 4).
Write the equation of the line that passes through (-6, 4) and is perpendicular to the given line.
Write the final answer in the slope-intercept form y = mx + b.
(The slope and y-intercept must be written as fractions, when needed).

#3:
Write the equation for the line perpendicular to
2x - 5y = 5 and passes through the point (-2, -5).
Enter the variable expression Ax + By separately from the constant term C.
Your response should be given in standard form where A, B and C are the smallest possible integers and A > 0.
Thanks so much.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
These explanations are quite lengthy, so here's a mini table of contents

#1
#2
#3

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"#1:
Write the equation of the line passing through the points listed below. Write the final answer in the slope-intercept form y = mx + b. If the slope (m) or the y-intercept (b) are not integers, fractions must be used.
(-1, 8); (9, 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

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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 (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 (,) 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.