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Gradient Intercept Form: Write an Equation>
Gradient Intercept Form: Write an Equation 1Gradient Intercept Form: Write an Equation 1
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Question 1 of 6
1. Question
Find the equation of the line in gradient intercept form.
- `y=` (1/2)`x+` (1)
Hint
Help VideoCorrect
Well Done!
Incorrect
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)
First, find the gradient of the line.The gradient is equivalent to the rise over the run.From `(-2,0)` rise up `1` unit, then run `2` units to the right to reach `(0,1)`
$$m=\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}=\frac{\color{#9a00c7}{1}}{\color{#00880a}{2}}$$`m=1/2`Next, find the y-intercept by finding the point where the line cuts the y-axis.
`b=1`Slot `m` and `b` into the gradient-intercept form.`y` `=` `m``x+``b` `y` `=` `1/2``x+``1` `y=1/2x +1` -
Question 2 of 6
2. Question
Find the equation of the line in gradient intercept form.
- `y=` (-3/2)`x+` (3)
Correct
Great Work!
Incorrect
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)
First, find the gradient of the line.The gradient is equivalent to the rise over the run.From `(0,3)` go down `3` units, then run `2` units to the right to reach `(2,0)`
$$m=\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}=\frac{\color{#9a00c7}{-3}}{\color{#00880a}{2}}$$`m=-3/2`Next, find the y-intercept by finding the point where the line cuts the y-axis.
`b=3`Slot `m` and `b` into the gradient-intercept form.`y` `=` `m``x+``b` `y` `=` `-3/2``x+``3` `y=-3/2x +3` -
Question 3 of 6
3. Question
Find the equation of the line in gradient intercept form.
- `y=` (1/2)`x+` (0)
Correct
Correct!
Incorrect
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)
First, find the gradient of the line.The gradient is equivalent to the rise over the run.From `(0,0)` rise up `1` unit, then run `2` units to the right to reach `(2,1)`
$$m=\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}=\frac{\color{#9a00c7}{1}}{\color{#00880a}{2}}$$`m=1/2`Next, find the y-intercept by finding the point where the line cuts the y-axis. The line passes through the origin.
`b=0`Slot `m` and `b` into the gradient-intercept form.`y` `=` `m``x+``b` `y` `=` `1/2``x+``0` `y` `=` `1/2``x` `y=1/2x` -
Question 4 of 6
4. Question
Find the equation of the line in gradient intercept form.
- `y=` (10/3)`x+` (-5)
Correct
Keep Going!
Incorrect
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)
First, find the gradient of the line.The gradient is equivalent to the rise over the run.From `(0,-5)` rise up `10` units, then run `3` units to the right to reach `(3,5)`
$$m=\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}=\frac{\color{#9a00c7}{10}}{\color{#00880a}{3}}$$`m=10/3`Next, find the y-intercept by finding the point where the line cuts the y-axis.
`b=-5`Slot `m` and `b` into the gradient-intercept form.`y` `=` `m``x+``b` `y` `=` `10/3``x+(``-5``)` `y` `=` `10/3``x``-5` `y=10/3x -5` -
Question 5 of 6
5. Question
Find the equation of the line in gradient intercept form.
- `y=` (-2/3)`x+` (-2)
Correct
Fantastic!
Incorrect
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)
First, find the gradient of the line.The gradient is equivalent to the rise over the run.From `(0,-2)` rise up `2` units, then run `3` units to the left to reach `(-3,0)`
$$m=\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}=\frac{\color{#9a00c7}{2}}{\color{#00880a}{-3}}$$`m=-2/3`Next, find the y-intercept by finding the point where the line cuts the y-axis.
`b=-2`Slot `m` and `b` into the gradient-intercept form.`y` `=` `m``x+``b` `y` `=` `-2/3``x+(``-2``)` `y` `=` `-2/3``x``-2` `y=-2/3x -2` -
Question 6 of 6
6. Question
Find the equation of the line in gradient intercept form.
- `y=` (-3)`x+` (2)
Correct
Exceptional!
Incorrect
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)
First, find the gradient of the line.The gradient is equivalent to the rise over the run.From `(0,2)` go down `3` units, then run `1` unit to the right to reach `(1,-1)`
$$m=\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}=\frac{\color{#9a00c7}{-3}}{\color{#00880a}{1}}$$`m=-3`Next, find the y-intercept by finding the point where the line cuts the y-axis.
`b=2`Slot `m` and `b` into the gradient-intercept form.`y` `=` `m``x+``b` `y` `=` `-3``x+``2` `y=-3x +2`
Quizzes
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- 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