Parallel Lines 2
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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`Hint
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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.`\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`
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Question 2 of 8
2. Question
Find the equation of the line parallel to `y=-2x-5` and passing through `(3,-4)`Hint
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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` `=` `-2``x-5` `m` `=` `-2` Slot in the gradient together with the point `(3,-4)` into the formula.`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` `y=-2x+2` -
Question 3 of 8
3. Question
Solve for `h`, given that the equations below are parallel.`2x-``h``y=5``3x+4y-8=0`Hint
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Gradient Intercept Form: `y=``m``x+``b`
- `m` is the gradient of the line
- `b` is the y-intercept (where the line cuts the y-axis)
Remember
Parallel lines have equal gradients.First, write the equations in gradient-intercept form.First equation:`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` Second equation:`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` Identify the gradients of the two equations.`y` `=` `2/h``x-5/h` `m` `=` `2/h` `y` `=` `(-3)/4``x+2` `m` `=` `(-3)/4` Since the two equations are parallel, their gradients must be equal.`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 `h=-2 2/3` -
Question 4 of 8
4. Question
Find the equation of the line parallel to `y=-5x-3` and passing through `(5,0)`
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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)x-3` `m` `=` `-5` Slot in the slope together with the point `color(royalblue)((5,0))` into the formula.`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` `y=-5x+25` -
Question 5 of 8
5. Question
Find the equation of the line parallel to `y=-x-2` and passing through `(2,0)`
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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)(-1)x-2` `m` `=` `-1` Slot in the slope together with the point `color(royalblue)((2,0))` into the formula.`y – color(royalblue)(y_1)` `=` `color(tomato)(m)(x- color(royalblue)(x_1))` `y – color(royalblue)((0))` `=` `color(tomato)((-1))(x- color(royalblue)(2))` `y-0` `=` `-1(x-2)` Simplify `y` `=` `-x+2` Distribute inside parenthesis `y=-x+2` -
Question 6 of 8
6. Question
Find the equation of the line parallel to `y=-2/3x-3` and passing through `(0,6)`
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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)(-2/3)x-3` `m` `=` `-2/3` Slot in the slope together with the point `color(royalblue)((0,6))` into the formula.`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=-2/3x+6` -
Question 7 of 8
7. Question
Find the equation of the line parallel to `y=7/3x-3` and passing through `(-3,1)`
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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)(7/3)x-3` `m` `=` `7/3` Slot in the slope together with the point `color(royalblue)((-3,1))` into the formula.`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=7/3x-6` -
Question 8 of 8
8. Question
Find the equation of the line parallel to `y=8/3x+2` and passing through `(-3,4)`
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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)(8/3)x+2` `m` `=` `8/3` Slot in the slope together with the point `color(royalblue)((-3,4))` into the formula.`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` `y=8/3x-4`
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 2
- 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
- Graph Linear Inequalities 1