Convert Standard Form and Slope Intercept Form

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Question 1 of 3

1. Question
Convert this equation to Gradient Intercept Form.

$3 x + 4 y - 20 = 0$ $3x+4y-20=0$
- 1. $y=-3/4x+5$
- 2. $y=4x-3$
- 3. $y=4/3x+5$
- 4. $y=-1/2x+3$
Hint

Help Video
Correct

Correct!
Incorrect
Help Video

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

$3x+4y-20$ $=$ $0$

$3x+4y-20$ $-3x$ $=$ $0$ $-3x$ Subtract $3x$ from both sides

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

$4y-20$ $+20$ $=$ $-3x$ $+20$ Add $20$ to both sides

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

Next, divide both sides by $4$ so that only $y$ remains on the left side.

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

$4y$ $divide4$ $=$ $(-3x+20)$ $divide4$ Divide both sides by $4$

$y$ $=$ $-3/4x+5$

$y=-3/4x+5$

Question 2 of 3

Graph

$x-2y-4=0$

Incorrect

Help Video

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

Question 3 of 3

Change the following into general format.

$y=(2/5)x -3$

(2x-5y-15=0)

$y$	$=$	$2/5x -3$

$y$ $xx 5$	$=$	$(2/5x-3)$ $xx 5$

$5y$	$=$	$2x-15$	Distribute $5$ inside the parenthesis
$5y$ $-5y$	$=$	$2x-15$ $-5y$	Subtract $5y$ from both sides
$0$	$=$	$2x-5y-15$
$2x-5y-15$	$=$	$0$	Interchange the sides

Convert Standard Form and Slope Intercept Form

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Quiz summary

Information

1. Question

Hint

Correct!

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

2. Question

Hint

Fantastic!

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

3. Question

Hint

Nice Job!

General Formula

Quizzes

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

$4y$	$=$	$-3x+20$
$4y$ $divide4$	$=$	$(-3x+20)$ $divide4$	Divide both sides by $4$
$y$	$=$	$-3/4x+5$

Convert Standard Form and Slope Intercept Form

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Quiz summary

Information

1. Question

Hint

Correct!

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

2. Question

Hint

Fantastic!

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

3. Question

Hint

Nice Job!

General Formula

Quizzes

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

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