Question 671693
Start with finding the slope
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slope = {{{(y1-y2)/(x1-x2) = (-8--3)/(2--4) = -5/6}}}
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Use either coordinate and the slope to solve for b, y-intercept
-8 = {{{-5/6}}}(2) + b
-8 = {{{-10/6}}} + b
b = -8 + {{{10/6}}} = {{{-8(6/6) + 10/6 = -48/6 + 10/6 = -38/6 = -19/3}}}
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Confirm using the other coordinate
y = {{{-5/6}}}(-4) + {{{-19/3}}}
y = {{{10/3 - 19/3 = -9/3 = -3}}}
That's correct! (-4, -3)
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So the equation for the line is...
y = {{{-5/6}}}x - {{{19/3}}}
written as a function
{{{highlight_green(f(x) = (-5/6)x - (19/3))}}}

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