Gradient of a Line 2
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Question 1 of 10
1. Question
Find the gradient of the line shown below?
- `m=` (2)
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Gradient Formula
`m=(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))`First, choose any two coordinates on the line to use in the gradient formula
We have chosen the points: `(0,4)` and `(-2,0)`Label the coordinates we chose from above`(color(forestgreen)(0),color(darkviolet)(4))=(color(forestgreen)(x_1),color(darkviolet)(y_1))``(color(forestgreen)(-2),color(darkviolet)(0))=(color(forestgreen)(x_2),color(darkviolet)(y_2))`Solve for the gradient `(m)` by substituting the two coordinates into the formula`m` `=` `(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))` Gradient formula `=` `(\color(darkviolet)(0)-\color(darkviolet)(4))/(color(forestgreen)(-2)-\color(forestgreen)(0))` Plug in the coordinates `=` `(-4)/(-2)` Evaluate `m` `=` `2` `-4 -: -2=2` `m=2` -
Question 2 of 10
2. Question
Find the gradient of the line shown below?
- `m=` (3)
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Gradient Formula
`m=(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))`First, choose any two coordinates on the line to use in the gradient formula
We have chosen the points: `(0,1)` and `(1,4)`Label the coordinates we chose from above`(color(forestgreen)(0),color(darkviolet)(1))=(color(forestgreen)(x_1),color(darkviolet)(y_1))``(color(forestgreen)(1),color(darkviolet)(4))=(color(forestgreen)(x_2),color(darkviolet)(y_2))`Solve for the gradient `(m)` by substituting the two coordinates into the formula`m` `=` `(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))` Gradient formula `=` `(\color(darkviolet)(4)-\color(darkviolet)(1))/(color(forestgreen)(1)-\color(forestgreen)(0))` Plug in the coordinates `=` `(3)/(1)` Evaluate `m` `=` `3` ` 3 -: 1 = 3 ` `m=3` -
Question 3 of 10
3. Question
Find the gradient of the line shown below?
- `m=` (5)
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Gradient Formula
`m=(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))`First, choose any two coordinates on the line to use in the gradient formula
We have chosen the points: `(0,-3)` and `(1,2)`Label the coordinates we chose from above`(color(forestgreen)(0),color(darkviolet)(-3))=(color(forestgreen)(x_1),color(darkviolet)(y_1))``(color(forestgreen)(1),color(darkviolet)(2))=(color(forestgreen)(x_2),color(darkviolet)(y_2))`Solve for the gradient `(m)` by substituting the two coordinates into the formula`m` `=` `(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))` Gradient formula `=` `(\color(darkviolet)(2)-\color(darkviolet)((-3)))/(color(forestgreen)(1)-\color(forestgreen)(0))` Plug in the coordinates `=` `(5)/(1)` Evaluate `m` `=` `5` `5 -: 1=5` `m=5` -
Question 4 of 10
4. Question
Find the gradient of the line shown below?
- `m=` (-2)
Correct
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Incorrect
Gradient Formula
`m=(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))`First, choose any two coordinates on the line to use in the gradient formula
We have chosen the points: `(-1,0)` and `(0,-2)`Label the coordinates we chose from above`(color(forestgreen)(-1),color(darkviolet)(0))=(color(forestgreen)(x_1),color(darkviolet)(y_1))``(color(forestgreen)(0),color(darkviolet)(-2))=(color(forestgreen)(x_2),color(darkviolet)(y_2))`Solve for the gradient `(m)` by substituting the two coordinates into the formula`m` `=` `(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))` Gradient formula `=` `(\color(darkviolet)(-2)-\color(darkviolet)(0))/(color(forestgreen)(0)-\color(forestgreen)((-1)))` Plug in the coordinates `=` `(-2)/(1)` Evaluate `m` `=` `-2` `-2 -: 1=-2` `m=-2` -
Question 5 of 10
5. Question
Find the gradient of the line shown below?
- `m=` (-4)
Correct
Keep Going!
Incorrect
Gradient Formula
`m=(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))`First, choose any two coordinates on the line to use in the gradient formula
We have chosen the points: `(0,1)` and `(1,-3)`Label the coordinates we chose from above`(color(forestgreen)(0),color(darkviolet)(1))=(color(forestgreen)(x_1),color(darkviolet)(y_1))``(color(forestgreen)(1),color(darkviolet)(-3))=(color(forestgreen)(x_2),color(darkviolet)(y_2))`Solve for the gradient `(m)` by substituting the two coordinates into the formula`m` `=` `(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))` Gradient formula `=` `(\color(darkviolet)(-3)-\color(darkviolet)(1))/(color(forestgreen)(1)-\color(forestgreen)(0))` Plug in the coordinates `=` `(-4)/(1)` Evaluate `m` `=` `-4` `-4 -: 1=-4` `m=-4` -
Question 6 of 10
6. Question
Find the gradient of the line shown below?
- `m=` (3/2)
Correct
Keep Going!
Incorrect
Gradient Formula
`m=(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))`First, choose any two coordinates on the line to use in the gradient formula
We have chosen the points: `(-2,2)` and `(0,5)`Label the coordinates we chose from above`(color(forestgreen)(-2),color(darkviolet)(2))=(color(forestgreen)(x_1),color(darkviolet)(y_1))``(color(forestgreen)(0),color(darkviolet)(5))=(color(forestgreen)(x_2),color(darkviolet)(y_2))`Solve for the gradient `(m)` by substituting the two coordinates into the formula`m` `=` `(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))` Gradient formula `=` `(\color(darkviolet)(5)-\color(darkviolet)(2))/(color(forestgreen)(0)-\color(forestgreen)((-2)))` Plug in the coordinates `=` `(3)/(2)` Evaluate `m` `=` `3/2` `m=3/2` -
Question 7 of 10
7. Question
Find the gradient of the line shown below?
- `m=` (1/3)
Correct
Keep Going!
Incorrect
Gradient Formula
`m=(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))`First, choose any two coordinates on the line to use in the gradient formula
We have chosen the points: `(3,0)` and `(0,-1)`Label the coordinates we chose from above`(color(forestgreen)(3),color(darkviolet)(0))=(color(forestgreen)(x_1),color(darkviolet)(y_1))``(color(forestgreen)(0),color(darkviolet)(-1))=(color(forestgreen)(x_2),color(darkviolet)(y_2))`Solve for the gradient `(m)` by substituting the two coordinates into the formula`m` `=` `(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))` Gradient formula `=` `(\color(darkviolet)(-1)-\color(darkviolet)(0))/(color(forestgreen)(0)-\color(forestgreen)(3))` Plug in the coordinates `=` `(-1)/(-3)` Evaluate `m` `=` `1/3` `-1 -: -3=1/3` `m=1/3` -
Question 8 of 10
8. Question
Find the gradient of the line shown below?
- `m=` (-4)
Correct
Keep Going!
Incorrect
Gradient Formula
`m=(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))`First, choose any two coordinates on the line to use in the gradient formula
We have chosen the points: `(0,-2)` and `(-1,2)`Label the coordinates we chose from above`(color(forestgreen)(0),color(darkviolet)(-2))=(color(forestgreen)(x_1),color(darkviolet)(y_1))``(color(forestgreen)(-1),color(darkviolet)(2))=(color(forestgreen)(x_2),color(darkviolet)(y_2))`Solve for the gradient `(m)` by substituting the two coordinates into the formula`m` `=` `(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))` Gradient formula `=` `(\color(darkviolet)(2)-\color(darkviolet)((-2)))/(color(forestgreen)(-1)-\color(forestgreen)(0))` Plug in the coordinates `=` `(4)/(-1)` Evaluate `m` `=` `-4` `4 -: -1=-4` `m=-4` -
Question 9 of 10
9. Question
Find the gradient of the line shown below?
- `m=` (3/4)
Correct
Keep Going!
Incorrect
Gradient Formula
`m=(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))`First, choose any two coordinates on the line to use in the gradient formula
We have chosen the points: `(4,1)` and `(0,-2)`Label the coordinates we chose from above`(color(forestgreen)(4),color(darkviolet)(1))=(color(forestgreen)(x_1),color(darkviolet)(y_1))``(color(forestgreen)(0),color(darkviolet)(-2))=(color(forestgreen)(x_2),color(darkviolet)(y_2))`Solve for the gradient `(m)` by substituting the two coordinates into the formula`m` `=` `(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))` Gradient formula `=` `(\color(darkviolet)(-2)-\color(darkviolet)(1))/(color(forestgreen)(0)-\color(forestgreen)(4))` Plug in the coordinates `=` `(-3)/(-4)` Evaluate `m` `=` `3/4` `-3 -: -4=3/4` `m=3/4` -
Question 10 of 10
10. Question
Find the gradient of the line shown below?
- `m=` (- 3/2)
Correct
Keep Going!
Incorrect
Gradient Formula
`m=(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))`First, choose any two coordinates on the line to use in the gradient formula
We have chosen the points: `(0,4)` and `(4,-2)`Label the coordinates we chose from above`(color(forestgreen)(0),color(darkviolet)(4))=(color(forestgreen)(x_1),color(darkviolet)(y_1))``(color(forestgreen)(4),color(darkviolet)(-2))=(color(forestgreen)(x_2),color(darkviolet)(y_2))`Solve for the gradient `(m)` by substituting the two coordinates into the formula`m` `=` `(\color(darkviolet)(y_2)-\color(darkviolet)(y_1))/(color(forestgreen)(x_2)-\color(forestgreen)(x_1))` Gradient formula `=` `(\color(darkviolet)(-2)-\color(darkviolet)(4))/(color(forestgreen)(4)-\color(forestgreen)(0))` Plug in the coordinates `=` `(-6)/(4)` Evaluate `m` `=` `- 3/2` `-6 -: 4 = – 3/2` `m=- 3/2`
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
- Gradient of a Line 1
- Gradient of a Line 2
- Gradient Intercept Form: Graph an Equation 1
- Gradient Intercept Form: Graph an Equation 2
- Gradient Intercept Form: Write an Equation 1
- Determine if a Point Lies on a Line
- Graph Linear Inequalities 1
- Graph Linear Inequalities 2
- Convert Between General Form and Gradient Intercept Form 1
- Convert Between General Form and Gradient Intercept Form 2
- Point Gradient and Two Point Formula 1
- Point Gradient and Two Point Formula 2
- Parallel Lines 1
- Parallel Lines 2
- Perpendicular Lines 1
- Perpendicular Lines 2