Question 68722
What is the equation of line through (8,6) and (2,-4), My answer is -4x+2y=-16, but I'm not sure thats for any help.

Here are the Steps that will help you find the equation through point (8,6) and (2, -4).

1. Find the slope of the line through the two point
{{{m = (y[2]-y[1])/(x[2]-x[1])}}}

Let (8, 6) = {{{x[1]}}}, {{{y[1]}}}
(2, -4) = {{{x[2]}}}, {{{y[2]}}}

<br>
{{{m = (-4-6)/(2-8)}}}
<br> {{{m = (-10)/(-6)}}} or {{{5/3}}}

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2. Write in slope - intercept form. Substitute the coordinates of either point for x and y and solve for b.
Let (x, y) = (2, -4)
y = mx + b
{{{-4 = (5/3)(2) + b}}}
{{{-4 = 10/3 + b}}}
{{{-4 - 10/3 = b}}}
{{{-12/3 - 10/3 = b}}}
{{{-22/3 = b}}}

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3. Substitute m = 5/3 and b = -22/3 to the slope-intercept form of the equation
y = mx + b
{{{y = (5/3)x - 22/3}}} >>> simplify.Multiply 3 both each term of the equation.
{{{highlight (3y = 5x - 22)}}}

<br>The Graph looks like this

<br>{{{graph (300, 300, -2, 14, -6, 8, (5/3)x-(22/3))}}}