Question 113515: Find an equation of the line through the given points. Write the equation in standard form.
Through (6,2) and (8,8).
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 (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 
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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.
However, the problem wants the answer in standard form. So let's convert the 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 3x 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 
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