Parallel Lines 1
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Question 1 of 8
1. Question
Are the two lines parallel?
Hint
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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`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. 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`
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Question 3 of 8
3. Question
Find the equation of the line parallel to `y=5-3x` and passing through `(4,-1)`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` `=` `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)`
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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)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)`
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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)(-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)`
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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)(-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)`
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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)(5/4)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)`
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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)(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`