Sarah R.

asked • 10/24/18

Write the equation of the line that passes through the points (1,-3) and (-3,1)

Autumn N.

first, find your slope using the formula m=y2-y1/x2-x1 (1-(-3)/ -3-1) 4/-4=-1 y=-1x+b solve for b from any given point b=-3-(-1)(-3) -2 y=-1x-2
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10/24/18

Autumn N.

You want to find the equation for a line that passes through the two points: (1,-3) and (-3,1). First of all, remember what the equation of a line is: y = mx+b Where: m is the slope, and b is the y-intercept First, let's find what m is, the slope of the line... The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal. For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form: So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (1,-3), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=1 and y1=-3. Also, let's call the second point you gave, (-3,1), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-3 and y2=1. Now, just plug the numbers into the formula for m above, like this: m= 1 - -3 -3 - 1 or... m= 4 -4 or... m=-1 So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this: y=-1x+b Now, what about b, the y-intercept? To find b, think about what your (x,y) points mean: (1,-3). When x of the line is 1, y of the line must be -3. (-3,1). When x of the line is -3, y of the line must be 1. Because you said the line passes through each one of these two points, right? Now, look at our line's equation so far: y=-1x+b. b is what we want, the -1 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (1,-3) and (-3,1). So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!. You can use either (x,y) point you want..the answer will be the same: (1,-3). y=mx+b or -3=-1 × 1+b, or solving for b: b=-3-(-1)(1). b=-2. (-3,1). y=mx+b or 1=-1 × -3+b, or solving for b: b=1-(-1)(-3). b=-2. See! In both cases we got the same value for b. And this completes our problem. The equation of the line that passes through the points (1,-3) and (-3,1) is y=-1x-2
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10/24/18

1 Expert Answer

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Ty D. answered • 10/24/18

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First find the slope = rise/run = y2 - y1/x2 - x1

m = (1 - (-3))/(-3 - 1) = 4/-4 = -1


Now we can substitute in the slope and either point to find b = y-intercept and write the equation:

y = mx + b

1 = -1(-3) + b

1 = 3 + b

-2 = b


The equation is y = -x -2.

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