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Convert Between General Form and Gradient Intercept Form>
Convert Between General Form and Gradient Intercept Form 2Convert Between General Form and Gradient Intercept Form 2
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Question 1 of 6
1. Question
Convert this equation to Gradient Intercept Form.
`10x+3y=2`
Hint
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Gradient Intercept Form: `y= color(tomato)(m)x+color(blue)(b)`
- `color(tomato)(m)` is the gradient of the line
- `color(blue)(b)` is the y-intercept (where the line cuts the y-axis)
First, make sure the `y`-term is alone on the left side.`10x+3y` `=` `2` `10x+3y color(red)(-10x)` `=` `2 color(red)(-10x)` Subtract `10x` from both sides `3y` `=` `2-10x` `3y` `=` `-10x+2` Rearrange Next, divide both sides by `3` so that only `y` remains on the left side.`3y` `=` `-10x+2` `3y color(red)(-:3)` `=` `(-10x+2) color(red)(-:3)` Divide both sides by `3` `y` `=` `-10/3x+2/3` `y=-10/3x+2/3` -
Question 2 of 6
2. Question
Convert this equation to Gradient Intercept Form.
`3x-y=3`
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Slope Intercept Form: `y= color(tomato)(m)x+color(blue)(b)`
- `color(tomato)(m)` is the gradient of the line
- `color(blue)(b)` is the y-intercept (where the line cuts the y-axis)
First, make sure the `y`-term is alone on the left side.`3x-y` `=` `3` `3x-y color(red)(-3x)` `=` `3 color(red)(-3x)` Subtract `3x` from both sides `-y` `=` `3-3x` `-y` `=` `-3x+3` Rearrange Next, divide both sides by `-1` so that only `y` remains on the left side.`-y` `=` `-3x+3` `-y color(red)(-: -1)` `=` `(-3x+3) color(red)(-: -1)` Divide both sides by `-1` `y` `=` `3x-3` `y=3x-3` -
Question 3 of 6
3. Question
Convert this equation to Gradient Intercept Form.
`5x-6y=2`
Hint
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Keep Going!
Incorrect
Gradient Intercept Form: `y= color(tomato)(m)x+color(blue)(b)`
- `color(tomato)(m)` is the gradient of the line
- `color(blue)(b)` is the y-intercept (where the line cuts the y-axis)
First, make sure the `y`-term is alone on the left side.`5x-6y` `=` `2` `5x-6y color(red)(-5x)` `=` `2 color(red)(-5x)` Subtract `5x` from both sides `-6y` `=` `2-5x` `-6y` `=` `-5x+2` Rearrange Next, divide both sides by `-6` so that only `y` remains on the left side.`-6y` `=` `-5x+2` `-6y color(red)(-: -6)` `=` `(-5x+2) color(red)(-: -6)` Divide both sides by `-6` `y` `=` `5/6x-1/3` `y=5/6x-1/3` -
Question 4 of 6
4. Question
Change the following into standard form.`y=(2/5)x -3`- (2x-5y-15=0)
Hint
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Incorrect
General Formula
`ax+by+c=0`Multiply both sides by `5` to remove the fraction, then arrange the terms to match the General Formula.`y` `=` `2/5x -3` `y``xx 5` `=` `(2/5x-3)``xx 5` `5y` `=` `2x-15` Distribute `5` inside the parenthesis `5y` `-5y` `=` `2x-15` `-5y` Subtract `5y` from both sides `0` `=` `2x-5y-15` `2x-5y-15` `=` `0` Interchange the sides `2x-5y-15=0` -
Question 5 of 6
5. Question
Convert this equation to Gradient Intercept Form.
`4x+2y=8`
Correct
Keep Going!
Incorrect
Gradient Intercept Form: `y= color(tomato)(m)x+color(blue)(b)`
- `color(tomato)(m)` is the gradient of the line
- `color(blue)(b)` is the y-intercept (where the line cuts the y-axis)
First, make sure the `y`-term is alone on the left side.`4x+2y` `=` `8` `4x+2y color(red)(-4x)` `=` `8 color(red)(-4x)` Subtract `4x` from both sides `2y` `=` `8-4x` `2y` `=` `-4x+8` Rearrange Next, divide both sides by `2` so that only `y` remains on the left side.`2y` `=` `-4x+8` `2y color(red)(-:2)` `=` `(-4x+8) color(red)(-:2)` Divide both sides by `2` `y` `=` `-2x+4` `y=-2x+4` -
Question 6 of 6
6. Question
Convert this equation to Gradient Intercept Form.
`3x-5y=-6`
Correct
Keep Going!
Incorrect
Gradient Intercept Form: `y= color(tomato)(m)x+color(blue)(b)`
- `color(tomato)(m)` is the gradient of the line
- `color(blue)(b)` is the y-intercept (where the line cuts the y-axis)
First, make sure the `y`-term is alone on the left side.`3x-5y` `=` `-6` `3x-5y color(red)(-3x)` `=` `-6 color(red)(-3x)` Subtract `3x` from both sides `-5y` `=` `-6-3x` `-5y` `=` `-3x-6` Rearrange Next, divide both sides by `-5` so that only `y` remains on the left side.`-5y` `=` `-3x-6` `-5y color(red)(-:-5)` `=` `(-3x-6) color(red)(-:-5)` Divide both sides by `-5` `y` `=` `3/5x+6/5` `y=3/5x+6/5`
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