Convert Standard Form and Slope Intercept Form 1

Question 1 of 6

Convert this equation to Slope Intercept Form.

3 x + 4 y - 20 = 0

$3x+4y-20=0$

1. $y = - \frac{3}{4} x + 5$ $y=-3/4x+5$
2. $y = 4 x - 3$ $y=4x-3$
3. $y = \frac{4}{3} x + 5$ $y=4/3x+5$
4. $y = - \frac{1}{2} x + 3$ $y=-1/2x+3$

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Slope Intercept Form: $y =$ $y=$ $m$ $m$ $x +$ $x+$ $b$ $b$

$m$ $m$ is the slope of the line
$b$ $b$ is the y-intercept (where the line cuts the y-axis)

First, make sure the

y

$y$ -term is alone on the left side.

$3 x + 4 y - 20$ $3x+4y-20$	$=$ $=$	$0$ $0$
$3 x + 4 y - 20 - 3 x$ $3x+4y-20 color(red)(-3x)$	$=$ $=$	$0 - 3 x$ $0 color(red)(-3x)$	Subtract $3 x$ $3x$ from both sides
$4 y - 20$ $4y-20$	$=$ $=$	$- 3 x$ $-3x$
$4 y - 20 + 20$ $4y-20 color(red)(+20)$	$=$ $=$	$- 3 x + 20$ $-3x color(red)(+20)$	Add $20$ $20$ to both sides
$4 y$ $4y$	$=$ $=$	$- 3 x + 20$ $-3x+20$

Next, divide both sides by

4

$4$ so that only

y

$y$ remains on the left side.

$4 y$ $4y$	$=$ $=$	$- 3 x + 20$ $-3x+20$
$4 y \div 4$ $4y color(red)(-:4)$	$=$ $=$	$(- 3 x + 20) \div 4$ $(-3x+20) color(red)(-:4)$	Divide both sides by $4$ $4$
$y$ $y$	$=$ $=$	$- \frac{3}{4} x + 5$ $-3/4x+5$

y = - \frac{3}{4} x + 5

$y=-3/4x+5$

Question 2 of 6

Convert this equation to Slope Intercept Form.

$4 x + 3 y = 7$ $4x+3y=7$

1. $y = - \frac{4}{3} x + \frac{7}{3}$ $y=-4/3x+7/3$
2. $y = - 4 x + 4$ $y=-4x+4$
3. $y = - 4 x + \frac{7}{3}$ $y=-4x+7/3$
4. $y = - 7 x + 4$ $y=-7x+4$

Incorrect

Slope Intercept Form: $y = m x + b$ $y= color(tomato)(m)x+color(blue)(b)$

$m$ $color(tomato)(m)$ is the slope of the line
$b$ $color(blue)(b)$ is the y-intercept (where the line cuts the y-axis)

First, make sure the

y

$y$ -term is alone on the left side.

$4 x + 3 y$ $4x+3y$	$=$ $=$	$7$ $7$
$4 x + 3 y - 4 x$ $4x+3y color(red)(-4x)$	$=$ $=$	$7 - 4 x$ $7 color(red)(-4x)$	Subtract $4 x$ $4x$ from both sides
$3 y$ $3y$	$=$ $=$	$7 - 4 x$ $7-4x$
$3 y$ $3y$	$=$ $=$	$- 4 x + 7$ $-4x+7$	Rearrange

Next, divide both sides by

3

$3$ so that only

y

$y$ remains on the left side.

$3 y$ $3y$	$=$ $=$	$- 4 x + 7$ $-4x+7$
$3 y \div 3$ $3y color(red)(-:3)$	$=$ $=$	$(- 4 x + 7) \div 3$ $(-4x+7) color(red)(-:3)$	Divide both sides by $3$ $3$
$y$ $y$	$=$ $=$	$- \frac{4}{3} x + \frac{7}{3}$ $-4/3x+7/3$

y = - \frac{4}{3} x + \frac{7}{3}

$y=-4/3x+7/3$

Question 3 of 6

Convert this equation to Slope Intercept Form.

$15 x + 8 y = 20$ $15x+8y=20$

1. $y = - \frac{15}{8} x + \frac{5}{8}$ $y=-15/8x+5/8$
2. $y = - \frac{15}{2} x + \frac{5}{2}$ $y=-15/2x+5/2$
3. $y = \frac{15}{8} x + \frac{5}{2}$ $y=15/8x+5/2$
4. $y = - \frac{15}{8} x + \frac{5}{2}$ $y=-15/8x+5/2$

Incorrect

Slope Intercept Form: $y = m x + b$ $y= color(tomato)(m)x+color(blue)(b)$

$m$ $color(tomato)(m)$ is the slope of the line
$b$ $color(blue)(b)$ is the y-intercept (where the line cuts the y-axis)

First, make sure the

y

$y$ -term is alone on the left side.

$15 x + 8 y$ $15x+8y$	$=$ $=$	$20$ $20$
$15 x + 8 y - 15 x$ $15x+8y color(red)(-15x)$	$=$ $=$	$20 - 15 x$ $20 color(red)(-15x)$	Subtract $15 x$ $15x$ from both sides
$8 y$ $8y$	$=$ $=$	$20 - 15 x$ $20-15x$
$8 y$ $8y$	$=$ $=$	$- 15 x + 20$ $-15x+20$	Rearrange

Next, divide both sides by

8

$8$ so that only

y

$y$ remains on the left side.

$8 y$ $8y$	$=$ $=$	$- 15 x + 20$ $-15x+20$
$8 y \div 8$ $8y color(red)(-:8)$	$=$ $=$	$(- 15 x + 20) \div 8$ $(-15x+20) color(red)(-:8)$	Divide both sides by $8$ $8$
$y$ $y$	$=$ $=$	$- \frac{15}{8} x + \frac{5}{2}$ $-15/8x+5/2$

y = - \frac{15}{8} x + \frac{5}{2}

$y=-15/8x+5/2$

Question 4 of 6

Convert this equation to Slope Intercept Form.

$11 x + 5 y = 56$ $11x+5y=56$

1. $y = \frac{11}{5} x + \frac{56}{5}$ $y=11/5x+56/5$
2. $y = - \frac{11}{5} x + \frac{56}{5}$ $y=-11/5x+56/5$
3. $y = - 11 x + \frac{56}{5}$ $y=-11x+56/5$
4. $y = - \frac{11}{5} x + 56$ $y=-11/5x+56$

Incorrect

Slope Intercept Form: $y = m x + b$ $y= color(tomato)(m)x+color(blue)(b)$

$m$ $color(tomato)(m)$ is the slope of the line
$b$ $color(blue)(b)$ is the y-intercept (where the line cuts the y-axis)

First, make sure the

y

$y$ -term is alone on the left side.

$11 x + 5 y$ $11x+5y$	$=$ $=$	$56$ $56$
$11 x + 5 y - 11 x$ $11x+5y color(red)(-11x)$	$=$ $=$	$56 - 11 x$ $56 color(red)(-11x)$	Subtract $11 x$ $11x$ from both sides
$5 y$ $5y$	$=$ $=$	$56 - 11 x$ $56-11x$
$5 y$ $5y$	$=$ $=$	$- 11 x + 56$ $-11x+56$	Rearrange

Next, divide both sides by

5

$5$ so that only

y

$y$ remains on the left side.

$5 y$ $5y$	$=$ $=$	$- 11 x + 56$ $-11x+56$
$5 y \div 5$ $5y color(red)(-:5)$	$=$ $=$	$(- 11 x + 56) \div 5$ $(-11x+56) color(red)(-:5)$	Divide both sides by $5$ $5$
$y$ $y$	$=$ $=$	$- \frac{11}{5} x + \frac{56}{5}$ $-11/5x+56/5$

y = - \frac{11}{5} x + \frac{56}{5}

$y=-11/5x+56/5$

Question 5 of 6

Convert this equation to Slope Intercept Form.

$8 x + 3 y = - 12$ $8x+3y=-12$

1. $y = \frac{8}{3} x + 4$ $y=8/3x+4$
2. $y - 8 x + 4$ $y-8x+4$
3. $y = - \frac{8}{3} x + \frac{4}{3}$ $y=-8/3x+4/3$
4. $y = - \frac{8}{3} x - 4$ $y=-8/3x-4$

Incorrect

Slope Intercept Form: $y = m x + b$ $y= color(tomato)(m)x+color(blue)(b)$

$m$ $color(tomato)(m)$ is the slope of the line
$b$ $color(blue)(b)$ is the y-intercept (where the line cuts the y-axis)

First, make sure the

y

$y$ -term is alone on the left side.

$8 x + 3 y$ $8x+3y$	$=$ $=$	$- 12$ $-12$
$8 x + 3 y - 8 x$ $8x+3y color(red)(-8x)$	$=$ $=$	$- 12 - 8 x$ $-12 color(red)(-8x)$	Subtract $8 x$ $8x$ from both sides
$3 y$ $3y$	$=$ $=$	$- 12 - 8 x$ $-12-8x$
$3 y$ $3y$	$=$ $=$	$- 8 x - 12$ $-8x-12$	Rearrange

Next, divide both sides by

3

$3$ so that only

y

$y$ remains on the left side.

$3 y$ $3y$	$=$ $=$	$- 8 x - 12$ $-8x-12$
$3 y \div 3$ $3y color(red)(-:3)$	$=$ $=$	$(- 8 x - 12) \div 3$ $(-8x-12) color(red)(-:3)$	Divide both sides by $3$ $3$
$y$ $y$	$=$ $=$	$- \frac{8}{3} x - 4$ $-8/3x-4$

y = - \frac{8}{3} x - 4

$y=-8/3x-4$

Question 6 of 6

Graph

x - 2 y - 4 = 0

$x-2y-4=0$

1.
2.
3.
4.

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Slope Intercept Form: $y =$ $y=$ $m$ $m$ $x +$ $x+$ $b$ $b$

$m$ $m$ is the slope of the line
$b$ $b$ is the y-intercept (where the line cuts the y-axis)

First, convert the equation to Slope Intercept Form.

$x - 2 y - 4$ $x-2y-4$	$=$ $=$	$0$ $0$
$x - 2 y - 4$ $x-2y-4$ $- x$ $-x$	$=$ $=$	$0$ $0$ $- x$ $-x$	Subtract $x$ $x$ from both sides
$- 2 y - 4$ $-2y-4$	$=$ $=$	$- x$ $-x$
$- 2 y - 4$ $-2y-4$ $+ 4$ $+4$	$=$ $=$	$- x$ $-x$ $+ 4$ $+4$	Add $4$ $4$ to both sides
$- 2 y$ $-2y$	$=$ $=$	$- x + 4$ $-x+4$
$2 y$ $2y$	$=$ $=$	$x - 4$ $x-4$	Convert the sign
$2 y$ $2y$ $\div 2$ $divide2$	$=$ $=$	$(x - 4)$ $(x-4)$ $\div 2$ $divide2$	Divide both sides by $2$ $2$

$y$ $y$	$=$ $=$	$\frac{1}{2} x - 2$ $1/2x-2$

Next, identify the slope and

y

$y$ -intercept.

For:

y =

$y=$ $\frac{1}{2}$ $1/2$

x

$x$ $- 2$ $-2$

The slope

(m)

$(m)$ is $\frac{1}{2}$ $1/2$ and the y-intercept

(b)

$(b)$ is $- 2$ $-2$ .

Now, plot the

y

$y$ -intercept $(- 2)$ $(-2)$

Use the slope $m = \frac{1}{2}$ $m=1/2$ to plot the next point.

The slope is equivalent to the rise over the run.

\frac{r i s e}{r u n} = \frac{1}{2}

$\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}=\frac{\color{#9a00c7}{1}}{\color{#00880a}{2}}$

From the

y

$y$ -intercept rise up $1$ $1$ unit, then run $2$ $2$ units to the right

Now we can graph the equation

Convert Standard Form and Slope Intercept Form 1

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Quiz summary

Information

1. Question

Hint

Correct!

Slope Intercept Form: $y =$ $y=$ $m$ $m$ $x +$ $x+$ $b$ $b$

2. Question

Hint

Keep Going!

Slope Intercept Form: $y = m x + b$ $y= color(tomato)(m)x+color(blue)(b)$

3. Question

Keep Going!

Slope Intercept Form: $y = m x + b$ $y= color(tomato)(m)x+color(blue)(b)$

4. Question

Hint

Keep Going!

Slope Intercept Form: $y = m x + b$ $y= color(tomato)(m)x+color(blue)(b)$

5. Question

Keep Going!

Slope Intercept Form: $y = m x + b$ $y= color(tomato)(m)x+color(blue)(b)$

6. Question

Hint

Fantastic!

Slope Intercept Form: $y =$ $y=$ $m$ $m$ $x +$ $x+$ $b$ $b$

Quizzes

Convert Standard Form and Slope Intercept Form 1

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Quiz summary

Information

1. Question

Hint

Correct!

Slope Intercept Form: y=y=y=mmmx+x+x+bbb

2. Question

Hint

Keep Going!

Slope Intercept Form: y=mx+by=mx+by= color(tomato)(m)x+color(blue)(b)

3. Question

Keep Going!

Slope Intercept Form: y=mx+by=mx+by= color(tomato)(m)x+color(blue)(b)

4. Question

Hint

Keep Going!

Slope Intercept Form: y=mx+by=mx+by= color(tomato)(m)x+color(blue)(b)

5. Question

Keep Going!

Slope Intercept Form: y=mx+by=mx+by= color(tomato)(m)x+color(blue)(b)

6. Question

Hint

Fantastic!

Slope Intercept Form: y=y=y=mmmx+x+x+bbb

Quizzes

Slope Intercept Form: $y =$ $y=$ $m$ $m$ $x +$ $x+$ $b$ $b$

Slope Intercept Form: $y = m x + b$ $y= color(tomato)(m)x+color(blue)(b)$

Slope Intercept Form: $y = m x + b$ $y= color(tomato)(m)x+color(blue)(b)$

Slope Intercept Form: $y = m x + b$ $y= color(tomato)(m)x+color(blue)(b)$

Slope Intercept Form: $y = m x + b$ $y= color(tomato)(m)x+color(blue)(b)$

Slope Intercept Form: $y =$ $y=$ $m$ $m$ $x +$ $x+$ $b$ $b$