Given two ordered pairs (1,-2) and (3,-8), what is the equation of the line in slope-intercept form?

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Given two ordered pairs (1,-2) and (3,-8), what is the equation of the line in slope-intercept form?

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Answer 1 · 2015-11-26T23:02:03

$y = - 3 x + 1$ $y=-3x+1$

Explanation:

The general equation for a line in slope-intercept form is:

$y = m x + b$ $y=mx+b$

where:
y = y-coordinate
m = slope
x = x-coordinate
b = y-intercept

To find the equation, first find the slope. The formula for slope is:

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m=(y_"2"-y_"1")/(x_"2"-x_"1")$

where:
m = slope
$(x_{1}, y_{1}) = (1, - 2)$ $(x_"1", y_"1")=(1,-2)$
$(x_{2}, y_{2}) = (3, - 8)$ $(x_"2", y_"2")=(3,-8)$

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m=(y_"2"-y_"1")/(x_"2"-x_"1")$

$m = \frac{(- 8) - (- 2)}{(3) - (1)}$ $m=((-8)-(-2))/((3)-(1))$

$m = - \frac{6}{2}$ $m=-6/2$

$m = - 3$ $m=-3$

Rewrite the equation:

$y = - 3 x + b$ $y=-3x+b$

Now substitute a known point into the equation to solve for $b$ $b$ :

$y = - 3 x + b$ $y=-3x+b$

$(- 2) = - 3 (1) + b$ $(-2)=-3(1)+b$

$- 2 = - 3 + b$ $-2=-3+b$

$1 = b$ $1=b$

Final answer:

$y = - 3 x + 1$ $y=-3x+1$

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Given two ordered pairs (1,-2) and (3,-8), what is the equation of the line in slope-intercept form?

1 Answer

Explanation:

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