Parallel Lines 1
Try VividMath Premium to unlock full access
Time limit: 0
Quiz summary
0 of 8 questions completed
Questions:
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
Information
–
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading...
You must sign in or sign up to start the quiz.
You have to finish following quiz, to start this quiz:
Loading...
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- Answered
- Review
-
Question 1 of 8
1. Question
Are the two lines parallel?
Hint
Help VideoCorrect
Great Work!
Incorrect
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`Hint
Help VideoCorrect
Fantastic!
Incorrect
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
3. Question
Find the equation of the line parallel to `y=5-3x` and passing through `(4,-1)`Hint
Help VideoCorrect
Great Work!
Incorrect
Point-Gradient Formula: `y -``y_1`` =``m``(x-``x_1``)`
- `m` is the gradient of the line
- `(x_1,y_1)` is the given point
Remember
Parallel lines have equal gradients.First, find the gradient of the given line.`y` `=` `5-3x` `y` `=` `-3``x+5` `m` `=` `-3` Slot in the gradient together with the point `(4,-1)` into the formula.`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=-3x+11` -
Question 4 of 8
4. Question
Find the equation of the line parallel to `y=-2x+2` and passing through `(-1,4)`
Correct
Keep Going!
Incorrect
Point Slope Form: `y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))`
- `color(tomato)(m)` is the slope of the line
- `(\color(royalblue)(x_1,y_1) )` is a point that lies on the line
Parallel lines have equal slopes.First, find the slope of the given line.`y` `=` `color(tomato)(-2)x+2` `m` `=` `-2` Slot in the slope together with the point `color(royalblue)((-1,4))` into the formula.`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=-2x+2` -
Question 5 of 8
5. Question
Find the equation of the line parallel to `y=-4x+2` and passing through `(0,4)`
Correct
Keep Going!
Incorrect
Point Slope Form: `y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))`
- `color(tomato)(m)` is the slope of the line
- `(\color(royalblue)(x_1,y_1) )` is a point that lies on the line
Parallel lines have equal slopes.First, find the slope of the given line.`y` `=` `color(tomato)(-4)x+2` `m` `=` `-4` Slot in the slope together with the point `color(royalblue)((0,4))` into the formula.`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=-4x+4` -
Question 6 of 8
6. Question
Find the equation of the line parallel to `y=-3x+2` and passing through `(-3,2)`
Correct
Keep Going!
Incorrect
Point Slope Form: `y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))`
- `color(tomato)(m)` is the slope of the line
- `(\color(royalblue)(x_1,y_1) )` is a point that lies on the line
Parallel lines have equal slopes.First, find the slope of the given line.`y` `=` `color(tomato)(-3)x+2` `m` `=` `-3` Slot in the slope together with the point `color(royalblue)((-3,2))` into the formula.`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=-3x-7` -
Question 7 of 8
7. Question
Find the equation of the line parallel to `y=5/4x+2` and passing through `(0,-1)`
Correct
Keep Going!
Incorrect
Point Slope Form: `y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))`
- `color(tomato)(m)` is the slope of the line
- `(\color(royalblue)(x_1,y_1) )` is a point that lies on the line
Parallel lines have equal slopes.First, find the slope of the given line.`y` `=` `color(tomato)(5/4)x+2` `m` `=` `5/4` Slot in the slope together with the point `color(royalblue)(0,-1))` into the formula.`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` `y=5/4x-1` -
Question 8 of 8
8. Question
Find the equation of the line parallel to `y=6/5x-1` and passing through `(-5,-1)`
Correct
Keep Going!
Incorrect
Point Slope Form: `y- color(royalblue)(y_1)= color(tomato)(m)(x- color(royalblue)(x_1))`
- `color(tomato)(m)` is the slope of the line
- `(\color(royalblue)(x_1,y_1) )` is a point that lies on the line
Parallel lines have equal slopes.First, find the slope of the given line.`y` `=` `color(tomato)(6/5)x-1` `m` `=` `6/5` Slot in the slope together with the point `color(royalblue)((-5,-1))` into the formula.`y – color(royalblue)(y_1)` `=` `color(tomato)(m)(x- color(royalblue)(x_1))` `y – color(royalblue)((-1))` `=` `color(tomato)((6/5))(x- color(royalblue)(-5))` `y+1` `=` `6/5(x+5)` Simplify `y+1` `=` `6/5x+6` Distribute inside parenthesis `y+1 color(crimson)(-1)` `=` `6/5x+6 color(crimson)(-1)` Subtract `1` from both sides `y` `=` `6/5x+5` `y=6/5x+5`
Quizzes
- Distance Between Two Points 1
- Distance Between Two Points 2
- Distance Between Two Points 3
- Midpoint of a Line 1
- Midpoint of a Line 2
- Midpoint of a Line 3
- Slope of a Line 1
- Slope of a Line 2
- Slope Intercept Form: Graph an Equation 1
- Slope Intercept Form: Graph an Equation 2
- Slope Intercept Form: Write an Equation 1
- Graph Linear Inequalities 1
- Convert Standard Form and Slope Intercept Form 1
- Convert Standard Form and Slope Intercept Form 2
- Point Slope Form 1
- Point Slope Form 2
- Parallel Lines 1
- Parallel Lines 2
- Perpendicular Lines 1
- Perpendicular Lines 2