Parallel Lines 2

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Geometry

Analytic Geometry

Parallel Lines

Parallel Lines 2

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Question 1 of 8

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

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

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

$C. y = \frac{2}{3} x - 4$ $\text(C.) y=2/3x-4$
- 1. $A$ $A$
- 2. $B$ $B$
- 3. $C$ $C$
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Parallel lines have equal gradients.

First, list down the gradients of each equation.

Note that in the gradient-intercept form $(y =$ $(y=$ $m$ $m$ $x + b)$ $x+b)$ , $m$ $m$ is the gradient.

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

$m_{A}$ $m_A$ $=$ $=$ $\frac{2}{3}$ $2/3$

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

$m_{B}$ $m_B$ $=$ $2/5$

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

$m_C$ $=$ $2/3$

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

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

Question 6 of 8

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

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

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. $y=7x-18$
3. $y=7x-3$
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. $y=8x-12$
2. $y=3x-8$
3. $y=3x+4/3$
4. $y=8/3x-4$

$y -$ $y_1$	$=$	$m$ $(x-$ $x_1$ $)$
$y -$ $(-4)$	$=$	$(-2)$ $(x-$ $3$ $)$
$y+4$	$=$	$-2(x-3)$	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
$y$	$=$	$-5x+25$

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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

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

	$m_{A}$ $m_A$	$=$ $=$	$\frac{2}{3}$ $2/3$

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

	$m_{B}$ $m_B$	$=$	$2/5$

$y – color(royalblue)(y_1)$	$=$	$color(tomato)(m)(x- color(royalblue)(x_1))$
$y – color(royalblue)((6))$	$=$	$color(tomato)((-2/3))(x- color(royalblue)(0))$
$y-6$	$=$	$(-2/3)(x-0)$	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
$y$	$=$	$8/3x-4$

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

	$m_C$	$=$	$2/3$

Parallel Lines 2

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