SOLUTION: The equation of the line through (8,6) and (2,-4) is A. 5x - 3y = 22 B. Y = 3/5x = 8/5 C. 3x = 4y = 48 D. -4x + 2y = -16

Question 87170: The equation of the line through (8,6) and (2,-4) is

A. 5x - 3y = 22
B. Y = 3/5x = 8/5
C. 3x = 4y = 48
D. -4x + 2y = -16

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)

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.

Since none of these answers match the equation in slope-intercept form, lets convert it to 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

Multiply both sides by the LCD 3

Distribute and multiply

Subtract 5x 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

Multiply both sides by -1 to make C a positive number

So the answer is A
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