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Question 1118579: A line passes through (-1,-13) and (1,3). Find the equation of this line in intercept form.
Found 4 solutions by josgarithmetic, Alan3354, ikleyn, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! A line passes through (-1,-13) and (1,3). Find the equation of this line in intercept form.
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| x y 1|
|-1 -13 1| = 0
| 1 3 1|
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x*(-13*1 - 3*1) - y*(-1*1 - 1*1) + 1*(-1*3 - 1*-13) = 0
-16x + 2y + 10 = 0
8x - y - 5 = 0
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y = 8x - 5
Answer by ikleyn(52781)  (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The matrix/determinant solution given by tutor @alan3354 is useful for more complex problems, but it seems a lot of work for this rather elementary problem.
Both of the other tutors who responded used a formula to find the slope of the line and then used the point-slope form of the equation to find the specific equation of the line in your example.
Those are valid ways to solve the problem. But I have some suggestions for alternative methods that you might want to try.
First: Finding the slope determined by the two given points.
There is a simple formula for slope:  .
Yes, a simple formula; but it is easy to get numbers in the wrong places and end up with the wrong slope, which of course makes any subsequent work you do on the problem a waste of time.
I always suggest to students that they at least mentally, if not on paper, make a sketch of the two points and use the sketch to find the slope by comparing the x and y coordinates of the two given points. Specifically, for the given points (-1,-13) and (1,3) in your problem, I think the safest way to find the slope is as follows:
Slope is the ratio of how fast the graph changes vertically and how fast it changes horizontally: "slope = rise / run". More specifically, I always think of it as measuring how far the graph goes up or down each time I move 1 unit to the right. So
(1) Since I always think of moving left to right, my "first" point will be the one that is farther left -- i.e., has the smaller x coordinate. So (-1,-13) is my "first" point and (1,3) is my second point.
(2) From the first point to the second, the x value changes from -1 to +1, a change of 2: the graph moved 2 units horizontally; the "run" is 2.
(3) From the first point to the second, the y value changes from -13 to +3, a change of 16: the graph moved up 16 units; the "rise" is 16.
(4) The slope is "rise"/"run" = 16/2 = 8.
You will make far fewer mistakes in finding slopes of lines if you use this method instead of plugging numbers into a magic formula.
Second: Finding the equation of the line
While use of the point-slope form of the equation of a line to finish finding the specific equation for a particular example is fine, in my experience more students find it easier to use the slope-intercept form. For your particular problem, it would go like this:
Plug the given x and y coordinates of one of the given points into the basic slope-intercept equation and solve for b:
Now you have both the slope and the y-intercept; the equation of the line is y = 8x-5.
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