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Question 1206892: Indicate in standard form the equation of the line passing through the given points, writing the answer in the equation box below.
E ( - 2, 2), F (5, 1)
Found 3 solutions by MathLover1, Theo, josgarithmetic:
Answer by MathLover1(20849)   (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 
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.
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 ....write in standard form  , both sides multiply by
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the points are (-2,2), (5,1)
let x1,y1 = -2,2 and x2,y2 = 5,1
slope = (y2-y1)/(x2-x1) = (1-2)/(5+2) = -1/7
use one of the points to get the y-intercept.
general slope intercept form equation is y = mx + b
m is the slope
b is the y-intercept
when the slope is -1/7, equation becomes y = -1/7 * x + b
use (5,1) coordinate and replace y with 1 and x with 5 to get:
1 = -1/7 * 5 + b
solve for b to get:
b = 1 + 5/7 = 12/7
equation becomes y = -1/7 * x + 12/7.
that's the slope intercept form of the equation.
to get the standard form, do the following:
add -1/7 * x to both sides of the equation to get 1/7 * x + y = 12/7
multiply both sides of the equation by 7 to get x + 7y = 12
that's the standard form of the equation.
here's the graph.
note that the standard form and the slope intercept form of the equation draw the same line.
that's because they're equivalent.
the two speciied points are on the line.
they are (-2,2) and (5,1)
the slope intercept is (0,1.714) where 1.714 represents the fraction 12/7.
Answer by josgarithmetic(39617)  (Show Source):
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