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What is the equation of the line through points (2, 5) and (5, 7)?

1 Answer

Jul 28, 2016

$2 x - 3 y = - 11$ $color(green)(2x-3y=-11)$

Explanation:

A line passing through $(2, 5)$ $(2,5)$ and $(5, 7)$ $(5,7)$ has a slope of
$XXX m = \frac{Δ y}{Δ x} = \frac{7 - 5}{5 - 2} = \frac{2}{3}$ $color(white)("XXX")m=(Deltay)/(Deltax)=(7-5)/(5-2)=2/3$

Using the point $(2, 5)$ $(2,5)$ and this slope, the slope-point form for this line's equation is
$XXX y - 5 = \frac{2}{3} (x - 2)$ $color(white)("XXX")y-5=2/3(x-2)$

This can be rearranged as
$XXX 3 y - 15 = 2 x - 4$ $color(white)("XXX")3y-15=2x-4$
or (in standard form)
$XXX 2 x - 3 y = - 11$ $color(white)("XXX")2x-3y=-11$

Here's the graph that helps verify this result:
enter image source here

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