Question 171331
i was going to quit but your plea struck a chord.
your problem:
you have two points:
(3,-12)
(-4,2)
with these two points you can find the equation for the line passing through them as follows:
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the slope intercept form of the equation for a line is y = m*x + b
m is the slope
b is the y-intercept (value of y when x = 0).
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your points are coordinates where the first point of the pair is the x coordinate and the second point of the pair is the y coordinate.
general form is (x,y).
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general formula for finding the slope is:
m = (y2-y1)/(x2-x1)
let x1 = 3 and y1 = -12
let x2 = -4 and y2 = 2
formula becomes:
m = (2-(-12))/((-4)-3)
simplify:
m = 14/(-7) = -2
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your slope is -2
y = m*x + b becomes:
y = -2*x + b
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now you have to find the y intercept.
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you need to take one of those points (either one will do) and substitute in the equation.
we'll take the first 1.
the equation:
y = -2*x + b
becomes:
-12 = -2*(3) + b
-12 = -6 + b
-6 = b
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if we used the second pair of points, we should have come up with the same answer.
let's try:
we'll now take the second 1.
the equation:
y = -2*x + b
becomes:
2 = -2*(-4) + b
2 = 8 + b
-6 = b
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b was -6 in both cases.
we have solved for b and the equation now becomes:
y = -2*x -6
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if this equation is good, then both points should make the equation true.
let's use the first pair of points (3,-12)
y = -2*x - 6
becomes:
-12 = -2*3 -6
-12 = -6 -6
-12 = -12
first pair proves equation true
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lets use the second pair of points (-4,2)
y = -2*x - 6
becomes:
2 = -2*-4 -6
2 = 8-6
2 = 2
second pair proves equation true
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equation is:
y = -2*x-6
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graph of this equation is shown below:
{{{graph(800,800,-10,10,-10,10,-2x-6)}}}
note the y intercept is -6 which is the value of b we solved for earlier.
in the equation y = -2*x - 6, if we make x = 0, then we get y = -6.
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note the x intercept is -3.
in the equation y = -2*x - 6, if we make y = 0, then we get:
0 = -2*x - 6
which becomes:
-2*x = 6
-x = 6/2 = 3
x = -3
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everything checks out and the graph is good.