Convert Between General Form and Gradient Intercept Form 1

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Question 1 of 6

Convert this equation to Gradient 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. $y = - \frac{1}{2} x + 3$ $y=-1/2x+3$

Question 2 of 6

2. Question
Convert this equation to Gradient Intercept Form.

$4x+3y=7$
- 1. $y=-7x+4$
- 2. $y=-4/3x+7/3$
- 3. $y=-4x+4$
- 4. $y=-4x+7/3$
Hint

Help Video
Correct

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

$color(tomato)(m)$ is the gradient of the line

$color(blue)(b)$ is the y-intercept (where the line cuts the y-axis)

First, make sure the $y$ -term is alone on the left side.

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

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

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

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

Next, divide both sides by $3$ so that only $y$ remains on the left side.

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

$3y color(red)(-:3)$ $=$ $(-4x+7) color(red)(-:3)$ Divide both sides by $3$

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

$y=-4/3x+7/3$
Question 3 of 6

3. Question
Convert this equation to Gradient Intercept Form.

$15x+8y=20$
- 1. $y=-15/8x+5/2$
- 2. $y=15/8x+5/2$
- 3. $y=-15/2x+5/2$
- 4. $y=-15/8x+5/8$
Correct

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

$color(tomato)(m)$ is the gradient of the line

$color(blue)(b)$ is the y-intercept (where the line cuts the y-axis)

First, make sure the $y$ -term is alone on the left side.

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

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

$8y$ $=$ $20-15x$

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

Next, divide both sides by $8$ so that only $y$ remains on the left side.

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

$8y color(red)(-:8)$ $=$ $(-15x+20) color(red)(-:8)$ Divide both sides by $8$

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

$y=-15/8x+5/2$
Question 4 of 6

4. Question
Convert this equation to Gradient Intercept Form.

$11x+5y=56$
- 1. $y=11/5x+56/5$
- 2. $y=-11x+56/5$
- 3. $y=-11/5x+56$
- 4. $y=-11/5x+56/5$
Hint

Help Video
Correct

Keep Going!
Incorrect
Gradient Intercept Form: $y= color(tomato)(m)x+color(blue)(b)$

$color(tomato)(m)$ is the gradient of the line

$color(blue)(b)$ is the y-intercept (where the line cuts the y-axis)

First, make sure the $y$ -term is alone on the left side.

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

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

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

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

Next, divide both sides by $5$ so that only $y$ remains on the left side.

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

$5y color(red)(-:5)$ $=$ $(-11x+56) color(red)(-:5)$ Divide both sides by $5$

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

$y=-11/5x+56/5$
Question 5 of 6

5. Question
Convert this equation to Gradient Intercept Form.

$8x+3y=-12$
- 1. $y=-8/3x-4$
- 2. $y=-8/3x+4/3$
- 3. $y-8x+4$
- 4. $y=8/3x+4$
Correct

Keep Going!
Incorrect
Gradient Intercept Form: $y= color(tomato)(m)x+color(blue)(b)$

$color(tomato)(m)$ is the gradient of the line

$color(blue)(b)$ is the y-intercept (where the line cuts the y-axis)

First, make sure the $y$ -term is alone on the left side.

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

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

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

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

Next, divide both sides by $3$ so that only $y$ remains on the left side.

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

$3y color(red)(-:3)$ $=$ $(-8x-12) color(red)(-:3)$ Divide both sides by $3$

$y$ $=$ $-8/3x-4$

$y=-8/3x-4$

Question 6 of 6

Graph

$x-2y-4=0$

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

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

First, convert the equation to Gradient Intercept Form.

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

$y$	$=$	$1/2x-2$

Next, identify the gradient and

$y$ -intercept.

For:

$y=$ $1/2$

$x$ $-2$

The gradient

$(m)$ is $1/2$ and the y-intercept

$(b)$ is $-2$ .

Now, plot the

$y$ -intercept $(-2)$

Use the gradient $m=1/2$ to plot the next point.

The gradient is equivalent to the rise over the run.

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

From the

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

Now we can graph the equation

$3 x + 4 y - 20$ $3x+4y-20$	$=$ $=$	$0$ $0$
$3 x + 4 y - 20 - 3 x$ $3x+4y-20 color(red)(-3x)$	$=$ $=$	$0 - 3 x$ $0 color(red)(-3x)$	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
$4 y$ $4y$	$=$ $=$	$- 3 x + 20$ $-3x+20$

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

Convert Between General Form and Gradient Intercept Form 1

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Quiz summary

Information

1. Question

Hint

Correct!

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

2. Question

Hint

Keep Going!

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

3. Question

Keep Going!

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

4. Question

Hint

Keep Going!

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

5. Question

Keep Going!

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

6. Question

Hint

Fantastic!

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

Quizzes

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

$3y$	$=$	$-4x+7$
$3y color(red)(-:3)$	$=$	$(-4x+7) color(red)(-:3)$	Divide both sides by $3$
$y$	$=$	$-4/3x+7/3$

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

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

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

$5y$	$=$	$-11x+56$
$5y color(red)(-:5)$	$=$	$(-11x+56) color(red)(-:5)$	Divide both sides by $5$
$y$	$=$	$-11/5x+56/5$

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

Convert Between General Form and Gradient Intercept Form 1

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Quiz summary

Information

1. Question

Hint

Correct!

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

2. Question

Hint

Keep Going!

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

3. Question

Keep Going!

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

4. Question

Hint

Keep Going!

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

5. Question

Keep Going!

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

6. Question

Hint

Fantastic!

Gradient Intercept Form: y=y=mmx+x+bb

Quizzes

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

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

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

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

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

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