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Convert Between General Form and Gradient Intercept Form>
Convert Between General Form and Gradient Intercept Form 1Convert Between General Form and Gradient Intercept Form 1
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Question 1 of 6
1. Question
Convert this equation to Gradient Intercept Form.`3x+4y-20=0`Hint
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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, make sure the `y`-term is alone on the left side.`3x+4y-20` `=` `0` `3x+4y-20 color(red)(-3x)` `=` `0 color(red)(-3x)` Subtract `3x` from both sides `4y-20` `=` `-3x` `4y-20 color(red)(+20)` `=` `-3x color(red)(+20)` Add `20` to both sides `4y` `=` `-3x+20` Next, divide both sides by `4` so that only `y` remains on the left side.`4y` `=` `-3x+20` `4y color(red)(-:4)` `=` `(-3x+20) color(red)(-:4)` Divide both sides by `4` `y` `=` `-3/4x+5` `y=-3/4x+5` -
Question 2 of 6
2. Question
Convert this equation to Gradient Intercept Form.
`4x+3y=7`
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.`4x+3y` `=` `7` `4x+3y color(red)(-4x)` `=` `7 color(red)(-4x)` Subtract `4x` from both sides `3y` `=` `7-4x` `3y` `=` `-4x+7` Rearrange Next, divide both sides by `3` so that only `y` remains on the left side.`3y` `=` `-4x+7` `3y color(red)(-:3)` `=` `(-4x+7) color(red)(-:3)` Divide both sides by `3` `y` `=` `-4/3x+7/3` `y=-4/3x+7/3` -
Question 3 of 6
3. Question
Convert this equation to Gradient Intercept Form.
`15x+8y=20`
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.`15x+8y` `=` `20` `15x+8y color(red)(-15x)` `=` `20 color(red)(-15x)` Subtract `15x` from both sides `8y` `=` `20-15x` `8y` `=` `-15x+20` Rearrange Next, divide both sides by `8` so that only `y` remains on the left side.`8y` `=` `-15x+20` `8y color(red)(-:8)` `=` `(-15x+20) color(red)(-:8)` Divide both sides by `8` `y` `=` `-15/8x+5/2` `y=-15/8x+5/2` -
Question 4 of 6
4. Question
Convert this equation to Gradient Intercept Form.
`11x+5y=56`
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.`11x+5y` `=` `56` `11x+5y color(red)(-11x)` `=` `56 color(red)(-11x)` Subtract `11x` from both sides `5y` `=` `56-11x` `5y` `=` `-11x+56` Rearrange Next, divide both sides by `5` so that only `y` remains on the left side.`5y` `=` `-11x+56` `5y color(red)(-:5)` `=` `(-11x+56) color(red)(-:5)` Divide both sides by `5` `y` `=` `-11/5x+56/5` `y=-11/5x+56/5` -
Question 5 of 6
5. Question
Convert this equation to Gradient Intercept Form.
`8x+3y=-12`
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.`8x+3y` `=` `-12` `8x+3y color(red)(-8x)` `=` `-12 color(red)(-8x)` Subtract `8x` from both sides `3y` `=` `-12-8x` `3y` `=` `-8x-12` Rearrange Next, divide both sides by `3` so that only `y` remains on the left side.`3y` `=` `-8x-12` `3y color(red)(-:3)` `=` `(-8x-12) color(red)(-:3)` Divide both sides by `3` `y` `=` `-8/3x-4` `y=-8/3x-4` -
Question 6 of 6
6. Question
Graph `x-2y-4=0`Hint
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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, convert the equation to Gradient Intercept Form.`x-2y-4` `=` `0` `x-2y-4` `-x` `=` `0` `-x` Subtract `x` from both sides `-2y-4` `=` `-x` `-2y-4` `+4` `=` `-x` `+4` Add `4` to both sides `-2y` `=` `-x+4` `2y` `=` `x-4` Convert the sign `2y``divide2` `=` `(x-4)``divide2` Divide both sides by `2` `y` `=` `1/2x-2` Next, identify the gradient and `y`-intercept.For: `y=``1/2``x``-2`The gradient `(m)` is `1/2` and the y-intercept `(b)` is `-2`.Now, plot the `y`-intercept `(-2)`
Use the gradient `m=1/2` to plot the next point.The gradient is equivalent to the rise over the run.$$\frac{\color{#9a00c7}{rise}}{\color{#00880a}{run}}=\frac{\color{#9a00c7}{1}}{\color{#00880a}{2}}$$From the `y`-intercept rise up `1` unit, then run `2` units to the right
Now we can graph the equation
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