Parallel Lines 2

Topics

Algebra 2

Linear Equations and Graphs

Parallel Lines

Parallel Lines 2

Try VividMath Premium to unlock full access

Start Free Trial

Lets see your results!

Points

Score

Time

Retry Quiz

Answered
Review

Question 1 of 8

1. Question
Which pair of equations can be graphed into two parallel lines?

$\text(A.) y=2/3x+7$

$\text(B.) y=2/5x+7$

$\text(C.) y=2/3x-4$
- 1. $A$
- 2. $B$
- 3. $C$
Hint

Help Video
Correct

Nice Job!
Incorrect
Need Text
Play
Current Time 0:00
/
Duration Time 0:00
Remaining Time -0:00
Stream TypeLIVE
Loaded: 0%
Progress: 0%
0:00
Fullscreen
Video Acceleration:
On
Off

00:00
Mute
Playback Rate
1x
2x
1.5x
1.25x
1x
0.75x
0.5x
Subtitles
subtitles off
Captions
captions off
English
Chapters
Chapters

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.

$\text(A.)$ $y$ $=$ $2/3$ $x+7$

$m_A$ $=$ $2/3$

$\text(B.)$ $y$ $=$ $2/5$ $x+7$

$m_B$ $=$ $2/5$

$\text(C.)$ $y$ $=$ $2/3$ $x-4$

$m_C$ $=$ $2/3$

Identify which equations have equal gradients.

$m_A$ $=$ $m_C$ $=$ $2/3$

Therefore, equations $A$ and $C$ are parallel.

$\text(A.) y=2/3x+7$

$\text(C.) y=2/3x-4$

Question 2 of 8

Find the equation of the line parallel to

$y=-2x-5$ and passing through

$(3,-4)$

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

Question 3 of 8

Solve for

$h$ , given that the equations below are parallel.

$2x-$ $h$

$y=5$

$3x+4y-8=0$

1. $3/4$
2. $3$
3. $-4/3$
4. $-2 2/3$

Question 4 of 8

Find the equation of the line parallel to $y=-5x-3$ and passing through $(5,0)$

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

Question 5 of 8

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

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

Question 6 of 8

Find the equation of the line parallel to $y=-2/3x-3$ and passing through $(0,6)$

1. $y=2x+9$
2. $y=-2x+2$
3. $y=-2x+18$
4. $y=-2/3x+6$

Question 7 of 8

Find the equation of the line parallel to $y=7/3x-3$ and passing through $(-3,1)$

1. $y=7/3x-6$
2. $y=7x-3$
3. $y=7x-18$
4. $y=3x-6$

Question 8 of 8

Find the equation of the line parallel to $y=8/3x+2$ and passing through $(-3,4)$

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

$y -$ $y_1$	$=$	$m$ $(x-$ $x_1$ $)$
$y -$ $(-4)$	$=$	$(-2)$ $(x-$ $3$ $)$
$y+4$	$=$	$-2(x-3)$	Simplify
$y+4$	$=$	$-2x+6$	Distribute inside parenthesis
$y+4$ $-4$	$=$	$-2x+6$ $-4$	Subtract $4$ from both sides
$y$	$=$	$-2x+2$

$2x-hy$	$=$	$5$
$2x-hy$ $-2x$	$=$	$5$ $-2x$	Subtract $2x$ from both sides.
$-hy$	$=$	$-2x+5$
$hy$	$=$	$2x-5$	Convert the sign.
$hy$ $divide h$	$=$	$(2x-5)$ $divide h$	Divide both sides by $h$ .

$y$	$=$	$2/hx-5/h$


$3x+4y-8$	$=$	$0$
$3x+4y-8$ $-(3x-8)$	$=$	$0$ $-(3x-8)$	Subtract $3x-8$ from both sides.
$4y$	$=$	$-3x+8$
$4y$ $divide 4$	$=$	$(-3x+8)$ $divide 4$	Divide both sides by $4$ .

$y$	$=$	$(-3)/4x+2$

$2/h$	$=$	$(-3)/4$

$2times4$	$=$	$-3timesh$	Cross multiply
$8$	$=$	$-3h$
$8$ $divide(-3)$	$=$	$-3h$ $divide(-3)$	Divide both sides by $-3$

$-8/3$	$=$	$h$

$h$	$=$	$-2 2/3$	Simplify

$y – color(royalblue)(y_1)$	$=$	$color(tomato)(m)(x- color(royalblue)(x_1))$
$y – color(royalblue)((0))$	$=$	$color(tomato)((-5))(x- color(royalblue)(5))$
$y$	$=$	$-5(x-5)$	Simplify
$y$	$=$	$-5x+25$	Distribute inside parenthesis
$y$	$=$	$-5x+25$

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Nice Job!

2. Question

Hint

Correct!

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

Remember

3. Question

Hint

Well Done!

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

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

$y – color(royalblue)(y_1)$	$=$	$color(tomato)(m)(x- color(royalblue)(x_1))$
$y – color(royalblue)((6))$	$=$	$color(tomato)((-2/3))(x- color(royalblue)(0))$
$y-6$	$=$	$(-2/3)(x-0)$	Simplify
$y-6$	$=$	$-2/3x+0$	Distribute inside parenthesis
$y-6 color(crimson)(+6)$	$=$	$-2/3x color(crimson)(+6)$	Add $6$ from both sides
$y$	$=$	$-2/3x+6$

$y – color(royalblue)(y_1)$	$=$	$color(tomato)(m)(x- color(royalblue)(x_1))$
$y – color(royalblue)((1))$	$=$	$color(tomato)((7/3))(x- color(royalblue)(-3))$
$y-1$	$=$	$7/3(x-3)$	Simplify
$y-1$	$=$	$7/3x-7$	Distribute inside parenthesis
$y-1 color(crimson)(+1)$	$=$	$7/3x-7 color(crimson)(+1)$	Add $1$ from both sides
$y$	$=$	$7/3x-6$

$y – color(royalblue)(y_1)$	$=$	$color(tomato)(m)(x- color(royalblue)(x_1))$
$y – color(royalblue)((4))$	$=$	$color(tomato)((8/3))(x- color(royalblue)(-3))$
$y-4$	$=$	$8/3(x-3)$	Simplify
$y-4$	$=$	$8/3x-8$	Distribute inside parenthesis
$y-4 color(crimson)(+4)$	$=$	$8/3x-8 color(crimson)(+4)$	Add $4$ from both sides
$y$	$=$	$8/3x-4$

$\text(A.)$	$y$	$=$	$2/3$ $x+7$

	$m_A$	$=$	$2/3$

$\text(B.)$	$y$	$=$	$2/5$ $x+7$

	$m_B$	$=$	$2/5$

$\text(C.)$	$y$	$=$	$2/3$ $x-4$

	$m_C$	$=$	$2/3$

Parallel Lines 2

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Nice Job!

2. Question

Hint

Correct!

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

Remember

3. Question

Hint

Well Done!

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

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

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

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

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