Question

topic three: slope-intercept form & standard form

• now that you feel comfortable with slope-intercept form ($y = mx + b$), youre going to learn how to convert between slope-intercept form and standard form ($ax + by = c$)

information given	identify $m$ and $b$	slope-intercept form $y = mx + b$	standard form $ax + by = c$
$0 = 5y - x$	$m = \frac{1}{5}$, $b = 0$	<handwritten content>	<handwritten content>
$3x + 2y = 6$	$m = $, $b = $
$-30 + 10y = 20x$	$m = $, $b = $
$x - y = -2$	$m = $, $b = $
$4x + 3y = -9$	$m = $, $b = $

Explanation:

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Row 3: $3x + 2y = 6$

Step1: Isolate $y$ term

$2y = -3x + 6$

Step2: Solve for $y$

$y = -\frac{3}{2}x + 3$

Step3: Identify $m, b$, confirm standard form

$m=-\frac{3}{2}$, $b=3$; standard form is $3x+2y=6$

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Row 4: $-30 + 10y = 20x$

Step1: Isolate $y$ term

$10y = 20x + 30$

Step2: Solve for $y$

$y = 2x + 3$

Step3: Identify $m, b$, convert to standard form

$m=2$, $b=3$; $20x - 10y = -30$ or simplified $2x - y = -3$

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Row 5: $x - y = -2$

Step1: Isolate $y$ term

$-y = -x - 2$

Step2: Solve for $y$

$y = x + 2$

Step3: Identify $m, b$, confirm standard form

$m=1$, $b=2$; standard form is $x - y = -2$

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Row 6: $4x + 3y = -9$

Step1: Isolate $y$ term

$3y = -4x - 9$

Step2: Solve for $y$

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

Step3: Identify $m, b$, confirm standard form

$m=-\frac{4}{3}$, $b=-3$; standard form is $4x+3y=-9$

Answer:

Information Given	Identify $m$ and $b$	Slope-Intercept Form $y=mx+b$	Standard Form $Ax+By=C$
$0=5y-x$	$m=\frac{1}{5}, b=0$	$y=\frac{1}{5}x$	$x-5y=0$
$3x+2y=6$	$m=-\frac{3}{2}, b=3$	$y=-\frac{3}{2}x+3$	$3x+2y=6$
$-30+10y=20x$	$m=2, b=3$	$y=2x+3$	$2x-y=-3$ (or $20x-10y=-30$)
$x-y=-2$	$m=1, b=2$	$y=x+2$	$x-y=-2$
$4x+3y=-9$	$m=-\frac{4}{3}, b=-3$	$y=-\frac{4}{3}x-3$	$4x+3y=-9$