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

Question 2 of 6

Convert this equation to Gradient 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. $y = - 4 x + \frac{7}{3}$ $y=-4x+7/3$
3. $y = - 7 x + 4$ $y=-7x+4$
4. $y = - 4 x + 4$ $y=-4x+4$

Question 3 of 6

Convert this equation to Gradient Intercept Form.

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

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

Question 4 of 6

Convert this equation to Gradient 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. $y = - 11 x + \frac{56}{5}$ $y=-11x+56/5$
3. $y = - \frac{11}{5} x + \frac{56}{5}$ $y=-11/5x+56/5$
4. $y = - \frac{11}{5} x + 56$ $y=-11/5x+56$

Question 5 of 6

Convert this equation to Gradient Intercept Form.

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

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

Question 6 of 6

Graph

x - 2 y - 4 = 0

$x-2y-4=0$

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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
$4 y$ $4y$	$=$ $=$	$- 3 x + 20$ $-3x+20$

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

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

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

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

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

3. Question

Keep Going!

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

4. Question

Hint

Keep Going!

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

5. Question

Keep Going!

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

6. Question

Hint

Fantastic!

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

Quizzes

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

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

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=mx+by= color(tomato)(m)x+color(blue)(b)

3. Question

Keep Going!

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

4. Question

Hint

Keep Going!

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

5. Question

Keep Going!

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

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

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

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

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