Equations Of A Line

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Question 1 of 7

1. Question
Graph the lines $y = 3$ $y=3$ and $x = 4$ $x=4$
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A table of values is used to find the ordered pairs $($ $($ $x$ $x$ $,$ $,$ $y$ $y$ $)$ $)$ of points on a line

Start by working out the $y-values$ $\text(y-values)$ for each $x-value$ $\text(x-value)$ in the table of values.

$x$ $x$ $0$ $0$ $1$ $1$ $2$ $2$

$y$ $y$

Substitute the $x-values$ $\text(x-values)$ into the given equation to find the corresponding $y-value$ $\text(y-value)$

Because there is no $x$ $x$ in the equation $y = 3$ $y=3$ , the answer will not change even if $x$ $x$ does.

$x$ $x$ $0$ $0$ $1$ $1$ $2$ $2$

$y$ $y$ $3$ $3$ $3$ $3$ $3$ $3$

Now, we can plot the points given from the table of values

To graph the line, simply connect the plotted points

Do the same for $x = 4$ $x=4$ . Just like the first equation, no matter what $y-value$ $\text(y-value)$ we have,
the $x-value$ $\text(x-value)$ is equal to $4$ $4$ . This means that the line cuts through the $x-axis$ $\text(x-axis)$ .

To graph the line, simply connect the plotted points
Question 2 of 7

2. Question
Graph the line $y = 2 x + 1$ $y=2x+1$
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A table of values is used to find the ordered pairs $($ $($ $x$ $x$ $,$ $,$ $y$ $y$ $)$ $)$ of points on a line

Start by working out the $y-values$ $\text(y-values)$ for each $x-value$ $\text(x-value)$ in the table of values.

$x$ $x$ $0$ $0$ $1$ $1$ $2$ $2$

$y$ $y$

Substitute the $x-values$ $\text(x-values)$ into the given equation to find the corresponding $y-value$ $\text(y-value)$

For the $x-value = 0$ $\text(x-value)=0$

$y$ $y$ $=$ $=$ $2$ $2$ $x$ $x$ $+ 1$ $+1$ Given Equation

$y$ $y$ $=$ $=$ $2$ $2$ $(0)$ $(0)$ $+ 1$ $+1$ Plug in $x = 0$ $x=0$

$y$ $y$ $=$ $=$ $1$ $1$

We can now add $y = 1$ $y=1$ to the table under $x = 0$ $x=0$

$x$ $x$ $0$ $0$ $1$ $1$ $2$ $2$

$y$ $y$ $1$ $1$

Repeat this process for each $x-value$ $\text(x-value)$

$x$ $x$ $0$ $0$ $1$ $1$ $2$ $2$

$y$ $y$ $1$ $1$ $3$ $3$ $5$ $5$

Now, we can plot the points given from the table of values

To graph the line, simply connect the plotted points
Question 3 of 7

3. Question
Find the equation of the line
- 1. $y = x + 1$ $y=x+1$
- 2. $y = 2 x$ $y=2x$
- 3. $y = 2 x - 1$ $y=2x-1$
- 4. $y = x$ $y=x$
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A table of values is used to find the ordered pairs $($ $($ $x$ $x$ $,$ $,$ $y$ $y$ $)$ $)$ of points on a line

Find the ordered pairs $($ $($ $x$ $x$ $,$ $,$ $y$ $y$ $)$ $)$ from the line.

$x$ $x$ $0$ $0$ $1$ $1$ $2$ $2$

$y$ $y$ $0$ $0$ $2$ $2$ $4$ $4$

Find the multiplier from the difference of consecutive $y$ $y$ values.

$2$ $2$ $-$ $-$ $0$ $0$ $=$ $=$ $2$ $2$

$4$ $4$ $-$ $-$ $2$ $2$ $=$ $=$ $2$ $2$ Multiplier is $2$ $2$

Write a formula with the multiplier $(2)$ $(2)$ and let $b$ $b$ be the constant.

$y =$ $y=$ $2$ $2$ $x \pm$ $x +-$ $b$ $b$

Since the line passes through the origin, $b = 0$ $b=0$ .

This means the equation of the line is $y = 2 x$ $y=2x$ .

$y = 2 x$ $y=2x$
Question 4 of 7

4. Question
Find the equation of the line
- 1. $y = 2 x$ $y=2x$
- 2. $y = 2 x - 1$ $y=2x-1$
- 3. $y = 2 x + 1$ $y=2x+1$
- 4. $y = x$ $y=x$
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A table of values is used to find the ordered pairs $($ $($ $x$ $x$ $,$ $,$ $y$ $y$ $)$ $)$ of points on a line

Find the ordered pairs $($ $($ $x$ $x$ $,$ $,$ $y$ $y$ $)$ $)$ from the line.

$x$ $x$ $0$ $0$ $1$ $1$ $2$ $2$

$y$ $y$ $1$ $1$ $3$ $3$ $5$ $5$

Find the multiplier from the difference of consecutive $y$ $y$ values.

$3$ $3$ $-$ $-$ $1$ $1$ $=$ $=$ $2$ $2$

$5$ $5$ $-$ $-$ $3$ $3$ $=$ $=$ $2$ $2$ Multiplier is $2$ $2$

Write a formula with the multiplier $(2)$ $(2)$ and let $b$ $b$ be the constant.

$y =$ $y=$ $2$ $2$ $x \pm$ $x +-$ $b$ $b$

Since the line cuts through the $y-axis$ $\text(y-axis)$ at $1$ $1$ , $b = 1$ $b=1$ .

This means the equation of the line is $y = 2 x + 1$ $y=2x+1$ .

$y = 2 x + 1$ $y=2x+1$
Question 5 of 7

5. Question
Find the equation of the line
- 1. $y = - 2 x + 4$ $y=-2x+4$
- 2. $y = - 2 x$ $y=-2x$
- 3. $y = 2 x - 1$ $y=2x-1$
- 4. $y = 2 x + 1$ $y=2x+1$
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A table of values is used to find the ordered pairs $($ $($ $x$ $x$ $,$ $,$ $y$ $y$ $)$ $)$ of points on a line

Find the ordered pairs $($ $($ $x$ $x$ $,$ $,$ $y$ $y$ $)$ $)$ from the line.

$x$ $x$ $0$ $0$ $1$ $1$ $2$ $2$

$y$ $y$ $4$ $4$ $2$ $2$ $0$ $0$

Find the multiplier from the difference of consecutive $y$ $y$ values.

$2$ $2$ $-$ $-$ $4$ $4$ $=$ $=$ $- 2$ $-2$

$0$ $0$ $-$ $-$ $2$ $2$ $=$ $=$ $- 2$ $-2$ Multiplier is $- 2$ $-2$

Write a formula with the multiplier $(- 2)$ $(-2)$ and let $b$ $b$ be the constant.

$y =$ $y=$ $- 2$ $-2$ $x \pm$ $x +-$ $b$ $b$

Since the line cuts through the $y-axis$ $\text(y-axis)$ at $4$ $4$ , $b = 4$ $b=4$ .

This means the equation of the line is $y = - 2 x + 4$ $y=-2x+4$ .

$y = - 2 x + 4$ $y=-2x+4$
Question 6 of 7

6. Question
Find the equation of the line
- 1. $y = 3 x$ $y=3x$
- 2. $y = x + 3$ $y=x+3$
- 3. $y = x + 3$ $y=x+3$
- 4. $y = 2 x - 3$ $y=2x-3$
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A table of values is used to find the ordered pairs $($ $x$ $,$ $y$ $)$ of points on a line

Find the ordered pairs $($ $x$ $,$ $y$ $)$ from the line.

$x$ $0$ $1$ $2$

$y$ $3$ $4$ $5$

Find the multiplier from the difference of consecutive $y$ values.

$5$ $-$ $4$ $=$ $1$

$4$ $-$ $3$ $=$ $1$ Multiplier is $1$

Write a formula with the multiplier $(1)$ and let $b$ be the constant.

$y=$ $1$ $x +-$ $b$

$y=x +-$ $b$

Since the line cuts through the $\text(y-axis)$ at $3$ , $b=3$ .

This means the equation of the line is $y=x+3$ .

$y=x+3$
Question 7 of 7

7. Question
Find the equation of the line
- 1. $y=1/2x$
- 2. $y=2x+1$
- 3. $y=2x-1$
- 4. $y=x$
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A table of values is used to find the ordered pairs $($ $x$ $,$ $y$ $)$ of points on a line

Find the ordered pairs $($ $x$ $,$ $y$ $)$ from the line.

$x$ $0$ $1$ $2$

$y$ $0$ $1/2$ $1$

Find the multiplier from the difference of consecutive $y$ values.

$1/2$ $-$ $0$ $=$ $1/2$

$1$ $-$ $1/2$ $=$ $1/2$ Multiplier is $1/2$

Write a formula with the multiplier $(1/2)$ and let $b$ be the constant.

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

Since the line cuts through the $\text(y-axis)$ at $0$ , $b=0$ .

This means the equation of the line is $y=1/2x$ .

$y=1/2x$

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Quiz summary

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1. Question

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2. Question

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3. Question

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4. Question

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5. Question

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6. Question

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7. Question

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Quizzes

$y$ $y$	$=$ $=$	$2$ $2$ $x$ $x$ $+ 1$ $+1$	Given Equation
$y$ $y$	$=$ $=$	$2$ $2$ $(0)$ $(0)$ $+ 1$ $+1$	Plug in $x = 0$ $x=0$
$y$ $y$	$=$ $=$	$1$ $1$

$2$ $2$ $-$ $-$ $0$ $0$	$=$ $=$	$2$ $2$
$4$ $4$ $-$ $-$ $2$ $2$	$=$ $=$	$2$ $2$	Multiplier is $2$ $2$

$3$ $3$ $-$ $-$ $1$ $1$	$=$ $=$	$2$ $2$
$5$ $5$ $-$ $-$ $3$ $3$	$=$ $=$	$2$ $2$	Multiplier is $2$ $2$

$2$ $2$ $-$ $-$ $4$ $4$	$=$ $=$	$- 2$ $-2$
$0$ $0$ $-$ $-$ $2$ $2$	$=$ $=$	$- 2$ $-2$	Multiplier is $- 2$ $-2$

$5$ $-$ $4$	$=$	$1$
$4$ $-$ $3$	$=$	$1$	Multiplier is $1$

$1/2$ $-$ $0$	$=$	$1/2$
$1$ $-$ $1/2$	$=$	$1/2$	Multiplier is $1/2$

$x$ $x$	$0$ $0$	$1$ $1$	$2$ $2$
$y$ $y$	$3$ $3$	$3$ $3$	$3$ $3$

$x$ $x$	$0$ $0$	$1$ $1$	$2$ $2$
$y$ $y$	$1$ $1$	$3$ $3$	$5$ $5$

$x$ $x$	$0$ $0$	$1$ $1$	$2$ $2$
$y$ $y$	$0$ $0$	$2$ $2$	$4$ $4$

$x$ $x$	$0$ $0$	$1$ $1$	$2$ $2$
$y$ $y$	$1$ $1$	$3$ $3$	$5$ $5$