SOLUTION: Write and equation of the line containing (5,-2) and (8,4) a. 2x-y=12 b.x-2y=9 c.2x+y=20

Question 107155This question is from textbook Algebra and Trigonometry Structure And Method
: Write and equation of the line containing (5,-2) and (8,4)
a. 2x-y=12
b.x-2y=9
c.2x+y=20 This question is from textbook Algebra and Trigonometry Structure And Method

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Finding the Equation of a Line

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 . Now reduce to get

Subtract from both sides to isolate y

Combine like terms and to get

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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.

Now lets convert the slope intercept equation into standard form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)

Convert from slope-intercept form (y = mx+b) to standard form (Ax+By = C)

Start with the given equation

Subtract 2x from both sides

Simplify

Multiply both sides by -1 to make the A coefficient positive (note: this step may be optional; it will depend on your teacher and/or textbook)

Distribute and simplify

The original equation (slope-intercept form) is equivalent to (standard form where A > 0)

The equation is in the form where , and

Now multiply both sides by -1 to make A positive

Distribute

So the equation is which means the answer is A)
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