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How do you write an equation of the line in standard form that is Parallel to 5y-4x=15 and through (10,6)?

1 Answer

Oct 19, 2015

$4 x - 5 y = 10$ $4x-5y=10$

Explanation:

$5 y - 4 x = 15$ $5y-4x=15$ has a slope of $\frac{4}{5}$ $4/5$

The slope-point form of a linear equation is
$XXX (y - ˆ y) = m (x - ˆ x)$ $color(white)("XXX")(y-haty) = m(x-hatx)$
$XXXXXXX$ $color(white)("XXXXXXX")$ where $m$ $m$ is the slope and $(ˆ x, ˆ y)$ $(hatx,haty)$ is a point

For this example we have
$XXX (y - 6) = \frac{4}{5} (x - 10)$ $color(white)("XXX")(y-6) = 4/5(x-10)$

Simplifying:
$XXX y = \frac{4}{5} x - 8 + 6$ $color(white)("XXX")y=4/5x-8+6$

$XXX 5 y = 4 x - 10$ $color(white)("XXX")5y=4x-10$

Standard form is
$XXX A x + B y = C$ $color(white)("XXX")Ax+By=C$ with $A, B, C in ZZ, A>=0$

Converting to standard form:
$color(white)("XXX")4x-5y=10$

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