SOLUTION: what is the slope intercept form of the equation of the line that passes through the point (2,5) and (-3,-1)

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Question 1203630: what is the slope intercept form of the equation of the line that passes through the point (2,5) and (-3,-1)
Found 4 solutions by Edwin McCravy, Theo, greenestamps, Alan3354:
Answer by Edwin McCravy(20056) About Me  (Show Source):
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Use the slope formula

m%22%22=%22%22%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 with %28matrix%281%2C3%2Cx%5B1%5D%2C%22%2C%22%2Cy%5B1%5D%29%29%22%22=%22%22%28matrix%281%2C3%2C2%5E%22%22%2C%22%2C%22%2C5%29%29 and %28matrix%281%2C3%2Cx%5B2%5D%2C%22%2C%22%2Cy%5B2%5D%29%29%22%22=%22%22%28matrix%281%2C3%2C-3%5E%22%22%2C%22%2C%22%2C-1%29%29

Then use the point-slope form:

y-y%5B1%5D%22%22=%22%22m%28x-x%5B1%5D%29

Don't substitute anything for x or y, but only for m, x1 and y1.

Then simplify until you get it down to the slope-intercept form:

y%22%22=%22%22m%2Ax%22%22%2B%22%22b

Edwin

Answer by Theo(13342) About Me  (Show Source):
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slope intercept form of the equation of a straight lin is y = mx + b.
m is the slope
b is the y-intercept.

your two points are (2,5) and (-3,-1)
let (2,5) be (x1,y1)
let (-3,-1) be (x2,y2)

slope is equal to (y2-y1)/(x2-x1) = (-1-5)/(-3-2) = -6/-5 = 6/5.
straight line equation becomes y = 6/5 * x + b

to find the value of b, replace x and y with the value from one of the points and solve.
i chose (2,5)
y = 6/5 * x + b becomes 5 = 6/5 * 2 + b which becomes 5 = 2.4 + b.
solve for b to get b = 5 - 2.4 = 2.6.
the value of b is 2.6 and the equation becomes:
y = 6/5 * x + 2.6
since 6/5 = 1.2, the equation can also be shown as y = 1.2 * x + 2.6

replacing x with 2 gets y = 5
replacing x with -3 gets y = -1
this confirms the points are on the line.

a graph of the equation shows the same, as shown below.







Answer by greenestamps(13200) About Me  (Show Source):
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In my experience, I have seen many students plug numbers into the formula for finding the slope and getting the numbers in the wrong places, which of course leads to wrong answers to the problems.

I strongly encourage students to have a mental picture of the two given points and calculate the slope using the "rise over run" definition.

It's simpler if you always move left to right (in the positive direction). So given the two points (2,5) and (-3,-1) I would picture starting at (-3,-1) and moving to (2,5).

In moving from (-3,-1) to (2,5), I move 5 units in the positive x direction; in doing so I move from -1 to 5, a difference of 6, in the y direction. Then "rise over run" gives me 6/5 -- and I don't need to worry if I got all the numbers in the right places in a formula.

Once you have the slope of 6/5, there are many ways to get to the equation of the line. For me, the easiest is to use the slope-intercept form of a linear equation "y=mx+b" with one of the given (x,y) points to find b.

y = mx+b
5 = (6/5)(2)+b
5 = 12/5+b
b = 5-12/5 = 25/5-12/5 = 13/5

ANSWER: y = (6/5)x+13/5

Answer by Alan3354(69443) About Me  (Show Source):
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what is the slope intercept form of the equation of the line that passes through the point (2,5) and (-3,-1)
----------------
| x   y   1|
| 2   5   1| = 0
|-3  -1   1|

x*(5*1 - -1*1) - y*(2*1 - 1*-3) + 2*-1 - -3*5 = 0
6x - 5y + 13 = 0
5y = 6x + 13
y = (6/5)x + 13/5