SOLUTION: Find a general form equation for the line through the pair of points. (1,4) and (8,-2) I know I am supposed to use the equation Ax + By = C, but I don't know how to plug in

Question 93118: Find a general form equation for the line through the pair of points.
(1,4) and (8,-2)
I know I am supposed to use the equation Ax + By = C, but I don't know how to plug in for A, B, and C. Please help!! Thanks so much!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First lets find the slope through the points (,) and (,)

Start with the slope formula

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

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 (,)

Now if you want to convert it into standard form then...

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 7

Distribute and multiply

Add 6x to both sides

Simplify

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

The equation is in the form where , and

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