How do you write the equation in slope intercept form given (-2, -1), (4, -4)?

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How do you write the equation in slope intercept form given (-2, -1), (4, -4)?

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Answer 1 · 2016-03-31T02:13:42

$y = - \frac{1}{2} x - 2$ $y=-1/2x-2$
with slope $m = - \frac{1}{2}$ $m=-1/2$ and y-intercept $b = - 2$ $b=-2$

Explanation:

We start with the Two Point Form

$y - y_{1} = (\frac{y_{2} - y_{1}}{x_{2} - x_{1}}) (x - x_{1})$ $y-y_1=((y_2-y_1)/(x_2-x_1))(x-x_1)$

with $P_{2} (x_{2}, y_{2}) = (4, - 4)$ $P_2(x_2, y_2)=(4, -4)$
and $P_{1} (x_{1}, y_{1}) = (- 2, - 1)$ $P_1(x_1, y_1)=(-2, -1)$

Compute slope $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{- 4 - - 1}{4 - - 2} = - \frac{3}{6} = - \frac{1}{2}$ $m=(y_2-y_1)/(x_2-x_1)=(-4--1)/(4--2)=-3/6=-1/2$

$y - y_{1} = (\frac{y_{2} - y_{1}}{x_{2} - x_{1}}) (x - x_{1})$ $y-y_1=((y_2-y_1)/(x_2-x_1))(x-x_1)$

$y - - 1 = - \frac{1}{2} (x - - 2)$ $y--1=-1/2(x--2)$

$y = - \frac{1}{2} x - 1 - 1$ $y=-1/2x-1-1$

$y = - \frac{1}{2} x - 2$ $y=-1/2x-2" "$ the required equation

Kindly see the graph of $y = - \frac{1}{2} x - 2$ $y=-1/2x-2$ passing thru with $P_{2} (4, - 4)$ $P_2(4, -4)$ and $P_{1} (- 2, - 1)$ $P_1(-2, -1)$

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How do you write the equation in slope intercept form given (-2, -1), (4, -4)?

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