Parallel Lines 1

Topics

Algebra 2

Linear Equations and Graphs

Parallel Lines

Parallel Lines 1

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Question 1 of 8

1. Question
Are the two lines parallel?
- 1. No
- 2. Yes
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Parallel lines have the same gradients.

Gradient Intercept Form: $y=mx+b$

$m$ is the gradient of the line

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

The gradient is given by the coefficient of $x$ or the value of $m$ .

$y$ $=$ $2x+1$

$m$ $=$ $2$

$y$ $=$ $2x-3$

$m$ $=$ $2$

The two gradients are equal, so the lines are parallel.

The lines are parallel.
Question 2 of 8

2. Question
Which equations can be graphed into parallel lines?

$\text(A.) y=-3x+2$

$\text(B.) y=4-3x$

$\text(C.) y=-3+3x$

$\text(D.) 2y=-6x+8$
- 1. $A$
- 2. $D$
- 3. $B$
- 4. $C$
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Parallel lines have equal gradients.

First, list down the gradients of each equation.

Note that in the gradient-intercept form $(y=$ $m$ $x+b)$ , $m$ is the gradient. For D, divide the equation by $2$ .

$\text(A.)$ $y$ $=$ $-3$ $x+2$

$m_A$ $=$ $-3$

$\text(B.)$ $y$ $=$ $4$ $-3$ $x$

$m_B$ $=$ $-3$

$\text(C.)$ $y$ $=$ $3$ $x-3$

$m_C$ $=$ $3$

$\text(D.)$ $y$ $=$ $-3$ $x+4$

$m_D$ $=$ $-3$

Identify which equations have equal gradients.

$m_A$ $=$ $m_B$ $=$ $m_D$ $=$ $-3$

Therefore, equations $A$ , $B$ and $D$ are parallel.

$\text(A.) y=-3x+2$

$\text(B.) y=4-3x$

$\text(D.) 2y=-6x+8$

Question 3 of 8

Find the equation of the line parallel to

$y=5-3x$ and passing through

$(4,-1)$

1. $y=3x+13$
2. $y=3x-11$
3. $y=-3x+11$
4. $y=11x+3$

Question 4 of 8

Find the equation of the line parallel to $y=-2x+2$ and passing through $(-1,4)$

1. $y=2x+1$
2. $y=2x-2$
3. $y=2x+2$
4. $y=-2x+2$

Question 5 of 8

Find the equation of the line parallel to $y=-4x+2$ and passing through $(0,4)$

1. $y=-4x+4$
2. $y=-4x-4$
3. $y=4x+4$
4. $y=-4x-4$

Question 6 of 8

Find the equation of the line parallel to $y=-3x+2$ and passing through $(-3,2)$

1. $y=-3x-7$
2. $y=3x+5$
3. $y=3x-7$
4. $y=-3x+4$

Question 7 of 8

Find the equation of the line parallel to $y=5/4x+2$ and passing through $(0,-1)$

1. $y=-5x-9$
2. $y=5x-4$
3. $y=5/4x-1$
4. $y=4x-5$

Question 8 of 8

Find the equation of the line parallel to $y=6/5x-1$ and passing through $(-5,-1)$

1. $y=6x+25$
2. $y=-6x+5$
3. $y=5x+5/6$
4. $y=6/5x+5$

$y -$ $y_1$	$=$	$m$ $(x-$ $x_1$ $)$
$y -$ $(-1)$	$=$	$(-3)$ $(x-$ $4$ $)$
$y+1$	$=$	$-3(x-4)$	Simplify
$y+1$	$=$	$-3x+12$	Distribute inside parenthesis
$y+1$ $-1$	$=$	$-3x+12$ $-1$	Subtract $1$ from both sides
$y$	$=$	$-3x+11$

$y – color(royalblue)(y_1)$	$=$	$color(tomato)(m)(x- color(royalblue)(x_1))$
$y – color(royalblue)((4))$	$=$	$color(tomato)((-2))(x- color(royalblue)(-1))$
$y-4$	$=$	$-2(x+1)$	Simplify
$y-4$	$=$	$-2x-2$	Distribute inside parenthesis
$y-4 color(crimson)(+4)$	$=$	$-2x-2 color(crimson)(+4)$	Add $4$ from both sides
$y$	$=$	$-2x+2$

$y – color(royalblue)(y_1)$	$=$	$color(tomato)(m)(x- color(royalblue)(x_1))$
$y – color(royalblue)((4))$	$=$	$color(tomato)((-4))(x- color(royalblue)(0))$
$y-4$	$=$	$-4(x-0)$	Simplify
$y-4$	$=$	$-4x+0$	Distribute inside parenthesis
$y-4 color(crimson)(+4)$	$=$	$-4x color(crimson)(+4)$	Add $4$ from both sides
$y$	$=$	$-4x+4$

$y – color(royalblue)(y_1)$	$=$	$color(tomato)(m)(x- color(royalblue)(x_1))$
$y – color(royalblue)((2))$	$=$	$color(tomato)((-3))(x- color(royalblue)(-3))$
$y-2$	$=$	$-3(x+3)$	Simplify
$y-2$	$=$	$-3x-9$	Distribute inside parenthesis
$y-2 color(crimson)(+2)$	$=$	$-3x-9 color(crimson)(+2)$	Add $2$ from both sides
$y$	$=$	$-3x-7$

$y – color(royalblue)(y_1)$	$=$	$color(tomato)(m)(x- color(royalblue)(x_1))$
$y – color(royalblue)((-1))$	$=$	$color(tomato)((5/4))(x- color(royalblue)(0))$
$y+1$	$=$	$5/4(x-0)$	Simplify
$y+1$	$=$	$5/4x$	Distribute inside parenthesis
$y+1 color(crimson)(-1)$	$=$	$5/4x color(crimson)(-1)$	Subtract $1$ from both sides
$y$	$=$	$5/4x-1$

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Quiz summary

Information

1. Question

Hint

Great Work!

Gradient Intercept Form: $y=mx+b$

2. Question

Hint

Fantastic!

3. Question

Hint

Great Work!

Point-Gradient Formula: $y -$ $y_1$ $=$ $m$ $(x-$ $x_1$ $)$

Remember

4. Question

Keep Going!

Point Slope Form: $y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))$

5. Question

Keep Going!

Point Slope Form: $y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))$

6. Question

Keep Going!

Point Slope Form: $y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))$

7. Question

Keep Going!

Point Slope Form: $y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))$

8. Question

Keep Going!

Point Slope Form: $y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))$

Quizzes

$\text(A.)$	$y$	$=$	$-3$ $x+2$
	$m_A$	$=$	$-3$

$\text(B.)$	$y$	$=$	$4$ $-3$ $x$
	$m_B$	$=$	$-3$

$\text(C.)$	$y$	$=$	$3$ $x-3$
	$m_C$	$=$	$3$

$\text(D.)$	$y$	$=$	$-3$ $x+4$
	$m_D$	$=$	$-3$

Parallel Lines 1

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Quiz summary

Information

1. Question

Hint

Great Work!

Gradient Intercept Form: y=mx+by=mx+b

2. Question

Hint

Fantastic!

3. Question

Hint

Great Work!

Point-Gradient Formula: y-y -y1y_1= =mm(x-(x-x1x_1))

Remember

4. Question

Keep Going!

Point Slope Form: y-y1=m(x-x1)y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))

5. Question

Keep Going!

Point Slope Form: y-y1=m(x-x1)y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))

6. Question

Keep Going!

Point Slope Form: y-y1=m(x-x1)y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))

7. Question

Keep Going!

Point Slope Form: y-y1=m(x-x1)y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))

8. Question

Keep Going!

Point Slope Form: y-y1=m(x-x1)y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))

Quizzes

Gradient Intercept Form: $y=mx+b$

Point-Gradient Formula: $y -$ $y_1$ $=$ $m$ $(x-$ $x_1$ $)$

Point Slope Form: $y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))$

Point Slope Form: $y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))$

Point Slope Form: $y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))$

Point Slope Form: $y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))$

Point Slope Form: $y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))$