Gradient of a Line 1
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Question 1 of 9
1. Question
Find the gradient of the line between the points `A(1,4)` and `B(3,2)`
- `m=` (-1)
Hint
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Well Done!
Incorrect
The gradient `(m)` refers to the “gradient” or “slant” of a lineMethod OneGradient Formula
$$m=\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$To find the gradient `(m)`, measure the rise and run between two points on the line
From point `(3, 2)` to `(1, 4)` the rise is `2` units and the run is `-2` unitsThe run is negative as the run goes to the left`m` `=` $$\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$ `=` $$\frac{\color{#9a00c7}{2}}{\color{#00880a}{-2}}$$ `m` `=` `-1` `m=-1`Method TwoGradient Formula
$$m=\frac{\color{#9a00c7}{y_2}-\color{#9a00c7}{y_1}}{\color{#00880a}{x_2}-\color{#00880a}{x_1}}$$First, choose any two coordinates on the line to use in the gradient Formula
We have chosen the points: `(1,4)` and `(3,2)`Label the coordinates we chose from above`(``1``,``4``) = (``x_1``,``y_1``)``(``3``,``2``) = (``x_2``,``y_2``)`Solve for the gradient `(m)` by substituting the two coordinates into the formula`m` `=` $$\frac{\color{#9a00c7}{y_2}-\color{#9a00c7}{y_1}}{\color{#00880a}{x_2}-\color{#00880a}{x_1}}$$ Gradient Formula `=` $$\frac{\color{#9a00c7}{2}-\color{#9a00c7}{4}}{\color{#00880a}{3}-\color{#00880a}{1}}$$ Plug in the coordinates `=` `(-2)/(2)` Evaluate `m` `=` `-1` `-2 divide 2=-1` `m=-1` -
Question 2 of 9
2. Question
Find the gradient of the line shown below
- `m=` (3/2, 1.5)
Hint
Help VideoCorrect
Great Work!
Incorrect
The gradient `(m)` refers to the “Gradient” or “slant” of a lineMethod OneGradient Formula
$$m=\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$To find the gradient `(m)`, measure the rise and run between two points on the line
From point `(2, 2)` to `(4, 5)` the rise is `3` units and the run is `2` units`m` `=` $$\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$ `=` $$\frac{\color{#9a00c7}{3}}{\color{#00880a}{2}}$$ `m` `=` `3/2` `m=3/2`Method TwoGradient Formula
$$m=\frac{\color{#9a00c7}{y_2}-\color{#9a00c7}{y_1}}{\color{#00880a}{x_2}-\color{#00880a}{x_1}}$$First, choose any two coordinates on the line to use in the Gradient Formula
We have chosen the points: `(2,2)` and `(4,5)`Label the coordinates we chose from above`(``2``,``2``) = (``x_1``,``y_1``)``(``4``,``5``) = (``x_2``,``y_2``)`Solve for the gradient `(m)` by substituting the two coordinates into the formula`m` `=` $$\frac{\color{#9a00c7}{y_2}-\color{#9a00c7}{y_1}}{\color{#00880a}{x_2}-\color{#00880a}{x_1}}$$ Gradient Formula `=` $$\frac{\color{#9a00c7}{5}-\color{#9a00c7}{2}}{\color{#00880a}{4}-\color{#00880a}{2}}$$ Plug in the coordinates `=` `3/2` Evaluate `m=3/2` -
Question 3 of 9
3. Question
Find the gradient of the line shown below
- `m=` (2)
Hint
Help VideoCorrect
Nice Job!
Incorrect
The gradient `(m)` refers to the “gradient” or “slant” of a lineMethod OneGradient Formula
$$m=\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$To find the gradient `(m)`, measure the rise and run between two points on the line
From point `(-1, 0)` to `(0, 2)` the rise is `2` units and the run is `1` unit`m` `=` $$\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$ `=` $$\frac{\color{#9a00c7}{2}}{\color{#00880a}{1}}$$ `m` `=` `2` `m=2`Method TwoGradient Formula
$$m=\frac{\color{#9a00c7}{y_2}-\color{#9a00c7}{y_1}}{\color{#00880a}{x_2}-\color{#00880a}{x_1}}$$First, choose any two coordinates on the line to use in the Gradient Formula
We have chosen the points: `(0,2)` and `(-1,0)`Label the coordinates we chose from above`(``0``,``2``) = (``x_1``,``y_1``)``(``-1``,``0``) = (``x_2``,``y_2``)`Solve for the gradient `(m)` by substituting the two coordinates into the formula`m` `=` $$\frac{\color{#9a00c7}{y_2}-\color{#9a00c7}{y_1}}{\color{#00880a}{x_2}-\color{#00880a}{x_1}}$$ Gradient Formula `=` $$\frac{\color{#9a00c7}{0}-\color{#9a00c7}{2}}{\color{#00880a}{-1}-\color{#00880a}{0}}$$ Plug in the coordinates `=` `(-2)/(-1)` Evaluate `m` `=` `2` `-2 divide -1=2` `m=2` -
Question 4 of 9
4. Question
Find the gradient of the line shown below
- `m=` (2)
Hint
Help VideoCorrect
Correct!
Incorrect
The gradient `(m)` refers to the “gradient” or “slant” of a lineGradient Formula
$$m=\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$To find the gradient `(m)`, measure the rise and run between two points on the line
From point `(0, 0)` to `(1, 2)` the rise is `2` units and the run is `1` unit`m` `=` $$\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$ `=` $$\frac{\color{#9a00c7}{2}}{\color{#00880a}{1}}$$ `m` `=` `2` `m=2` -
Question 5 of 9
5. Question
Find the gradient of the line shown below
- `m=` (1)
Hint
Help VideoCorrect
Excellent!
Incorrect
The gradient `(m)` refers to the “gradient” or “slant” of a lineGradient Formula
$$m=\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$To find the gradient `(m)`, measure the rise and run between two points on the line
From point `(0, 0)` to `(2, 2)` the rise is `2` units and the run is `2` units`m` `=` $$\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$ `=` $$\frac{\color{#9a00c7}{2}}{\color{#00880a}{2}}$$ `m` `=` `1` `m=1` -
Question 6 of 9
6. Question
Find the gradient of the line shown below
- `m=` (1/4, 0.25)
Hint
Help VideoCorrect
Keep Going!
Incorrect
The gradient `(m)` refers to the “gradient” or “slant” of a lineGradient Formula
$$m=\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$To find the gradient `(m)`, measure the rise and run between two points on the line
From point `(0, 0)` to `(4, 1)` the rise is `1` unit and the run is `4` units`m` `=` $$\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$ `=` $$\frac{\color{#9a00c7}{1}}{\color{#00880a}{4}}$$ `m` `=` `1/4` `m=1/4` -
Question 7 of 9
7. Question
Find the gradient of the line shown below
- `m=` (-1/2, -0.5)
Hint
Help VideoCorrect
Fantastic!
Incorrect
The gradient `(m)` refers to the “gradient” or “slant” of a lineGradient Formula
$$m=\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$To find the gradient `(m)`, measure the rise and run between two points on the line
From point `(4, 0)` to `(0, 2)` the rise is `2` units and the run is `-4` units`m` `=` $$\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$ `=` $$\frac{\color{#9a00c7}{2}}{\color{#00880a}{-4}}$$ `=` `-2/4` `m` `=` `-1/2` Reduce to lowest terms `m=-1/2` -
Question 8 of 9
8. Question
Is the shape below a parallelogram?
Hint
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Excellent!
Incorrect
A parallelogram is a quadrilateral with opposite sides parallel. Parallel lines have the same gradients.Gradient Formula
$$m=\frac{\color{#9a00c7}{y_2}-\color{#9a00c7}{y_1}}{\color{#00880a}{x_2}-\color{#00880a}{x_1}}$$First, label the given coordinates`A(``1``,``2``) = (``x_1``,``y_1``)``B(``5``,``2``) = (``x_1``,``y_1``)``C(``3``,``-2``) = (``x_2``,``y_2``)``D(``-1``,``-2``) = (``x_2``,``y_2``)`Solve for the gradient `(m)` by substituting the pairs of coordinates for lines `AD` and `BC` into the formula$$m_{AD}$$ `=` $$\frac{\color{#9a00c7}{y_2}-\color{#9a00c7}{y_1}}{\color{#00880a}{x_2}-\color{#00880a}{x_1}}$$ `=` $$\frac{\color{#9a00c7}{-2}-\color{#9a00c7}{2}}{\color{#00880a}{-1}-\color{#00880a}{1}}$$ `=` $$\frac{\color{#9a00c7}{-4}}{\color{#00880a}{-2}}$$ $$m_{AD}$$ `=` $$2$$ $$m_{BC}$$ `=` $$\frac{\color{#9a00c7}{y_2}-\color{#9a00c7}{y_1}}{\color{#00880a}{x_2}-\color{#00880a}{x_1}}$$ `=` $$\frac{\color{#9a00c7}{-2}-\color{#9a00c7}{2}}{\color{#00880a}{3}-\color{#00880a}{5}}$$ `=` $$\frac{\color{#9a00c7}{-4}}{\color{#00880a}{-2}}$$ $$m_{BC}$$ `=` $$2$$ Identify whether the quadrilateral is a parallelogram.`m_(AD) = m_(BC)` so lines `AD` and `BC` are parallel, and therefore the given quadrilateral is a parallelogram.The quadrilateral is a parallelogram. -
Question 9 of 9
9. Question
Are the two lines parallel?
Hint
Help VideoCorrect
Nice Job!
Incorrect
Parallel lines have the same gradients.Gradient Formula
$$m=\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$To find the gradient `(m)`, measure the rise and run between two points on the lineBlack line: From point `(4, 0)` to `(0, 4)` the rise is `4` units and the run is `-4` units
`m` `=` $$\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$ `=` $$\frac{\color{#9a00c7}{4}}{\color{#00880a}{-4}}$$ `m` `=` `-1` Red line: From point `(-2, 0)` to `(0, -2)` the rise is `-2` units and the run is `2` units`m` `=` $$\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}$$ `=` $$\frac{\color{#9a00c7}{-2}}{\color{#00880a}{2}}$$ `m` `=` `-1` The two gradients are equal, so the lines are parallel.The lines are parallel.
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