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

$y=-3x+1$

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

$y=mx+b$

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:

$m=(y_"2"-y_"1")/(x_"2"-x_"1")$

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

$m=(y_"2"-y_"1")/(x_"2"-x_"1")$

$m=((-8)-(-2))/((3)-(1))$

$m=-6/2$

$m=-3$

Rewrite the equation:

$y=-3x+b$

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

$y=-3x+b$

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

$-2=-3+b$

$1=b$

Final answer:

$y=-3x+1$