Question 201702: Please help.
For the points (3,-2) and (-5,-4) find:
the slope between them and the equation of the line that passes through them
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! For the points (3,-2) and (-5,-4) find:
the slope between them and the equation of the line that passes through them.
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the slope of the line is given by the equation (y2-y1)/(x2-x1).
let (3,-2) = (x1,y1)
let (-5,-4) = (x2,y2)
x1 = 3
y1 = -2
x2 = -5
y2 = -4
(y2-y1) = (-4) - (-2) = (-2)
(x2-x1) = (-5) - (3) = (-8)
(y2-y1)/(x2-x1) = (-2)/(-8) = (-1)/(-4) = (1/4)
your slope is (1/4).
equation for a line is y = m*x + b where:
m is the slope
b is the y-intercept (value of y when x = 0).
to find b, you take one of the points that you were given and substitute for y and x and solve.
take the point (x2,y2) which equals (-5,-4).
you have:
y = -4
x = -5
m = (1/4) which was calculated earlier.
substitute for x and y in the general equation of y = m*x + b to get
-4 = (1/4)*(-5) + b
multiply both sides of the equation by 4 to get:
-16 = (1) * (-5) + 4*b
which equals
-16 = -5 + 4*b
add 5 to both sides of the equation to get:
-11 = 4*b
divide both sides of the equation by 4 to get:
b = (-11/4)
you have m which is (1/4) and you have b which is (-11/4)
your equation is
y = (1/4)*x + (-11/4)
which becomes
y = (1/4)*x - (11/4)
a graph of this equation will look like this:
your y intercept is (-11/4) which is the same as (-2.75). this is found by taking the general equation and making y = 0 and solving.
your x intercept is 11 which you find by taking the general equation and making x = 0 and solving.
both your original points are on this line as you can see from the graph.
your slope is (1/4) which you can find easily by taking the y intercept and the x intercept and solving for the slope.
the y intercept is (0,-11/4)
the x intercept is (11,0).
x1 = 0
y1 = -11/4
x2 = 11
y2 = 0
y2 - y1 = 0 - (-11/4) = 11/4
x2 - x1 = 11 - 0 = 11
(y2-y1) / (x2-x1) = (11/4) / 11 = (1/4) / 1 = (1/4).
everything checks out.
your slope is (1/4)
your equation is y = (1/4)*x - (11/4).
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