What is $3 x - 4 y = 12$ $3x-4y=12$ in slope-intercept form?

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What is $3 x - 4 y = 12$ $3x-4y=12$ in slope-intercept form?

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Answer 1 · 2016-09-29T03:57:34

$y = \frac{3}{4} x - 3$ $y = 3/4x-3$

Explanation:

Slope-intercept form means we are looking for an equation of the type $y = m x + b$ $y = mx+b$

Starting with $3 x - 4 y = 12$ $3x-4y=12$ , we can add $4 y$ $4y$ to each side, yielding
$3 x - 4 y + 4 y = 12 + 4 y$ $3x-4y+4y=12+4y$
and $- 4 y + 4 y = 0$ $-4y+4y = 0$ , so we are left with
$3 x = 12 + 4 y$ $3x=12+4y$
We now subtract 12 from both sides:
$3 x - 12 = 12 + 4 y - 12$ $3x-12=12+4y-12$
$12 - 12 = 0$ $12-12 = 0$ , leaving us with:
$3 x - 12 = 4 y$ $3x-12 = 4y$
We now divide by 4 on both sides:
$\frac{3 x - 12}{4} = \frac{4 y}{4}$ $(3x-12)/4 = (4y)/4$
We know $\frac{4 y}{4} = y$ $(4y)/4 = y$
On the left hand side, we can split $\frac{3 x - 12}{4}$ $(3x-12)/4$ into $\frac{3 x}{4} - \frac{12}{4}$ $(3x)/4 - 12/4$ .
Simplifying, we find $\frac{3}{4} x - 3 = y$ $3/4x - 3 = y$ , which is in slope intercept form, as requested.

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What is $3 x - 4 y = 12$ $3x-4y=12$ in slope-intercept form?

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