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Convert Standard Form and Slope Intercept Form 1Convert Standard Form and Slope Intercept Form 1
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Question 1 of 6
1. Question
Convert this equation to Slope Intercept Form.`3x+4y20=0`Hint
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Slope Intercept Form: `y=``m``x+``b`
 `m` is the slope of the line
 `b` is the yintercept (where the line cuts the yaxis)
First, make sure the `y`term is alone on the left side.`3x+4y20` `=` `0` `3x+4y20 color(red)(3x)` `=` `0 color(red)(3x)` Subtract `3x` from both sides `4y20` `=` `3x` `4y20 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 Slope Intercept Form.
`4x+3y=7`
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Slope Intercept Form: `y= color(tomato)(m)x+color(blue)(b)`
 `color(tomato)(m)` is the slope of the line
 `color(blue)(b)` is the yintercept (where the line cuts the yaxis)
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` `=` `74x` `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 Slope Intercept Form.
`15x+8y=20`
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Keep Going!
Incorrect
Slope Intercept Form: `y= color(tomato)(m)x+color(blue)(b)`
 `color(tomato)(m)` is the slope of the line
 `color(blue)(b)` is the yintercept (where the line cuts the yaxis)
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` `=` `2015x` `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 Slope Intercept Form.
`11x+5y=56`
Hint
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Slope Intercept Form: `y= color(tomato)(m)x+color(blue)(b)`
 `color(tomato)(m)` is the slope of the line
 `color(blue)(b)` is the yintercept (where the line cuts the yaxis)
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` `=` `5611x` `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 Slope Intercept Form.
`8x+3y=12`
Correct
Keep Going!
Incorrect
Slope Intercept Form: `y= color(tomato)(m)x+color(blue)(b)`
 `color(tomato)(m)` is the slope of the line
 `color(blue)(b)` is the yintercept (where the line cuts the yaxis)
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` `=` `128x` `3y` `=` `8x12` Rearrange Next, divide both sides by `3` so that only `y` remains on the left side.`3y` `=` `8x12` `3y color(red)(:3)` `=` `(8x12) color(red)(:3)` Divide both sides by `3` `y` `=` `8/3x4` `y=8/3x4` 
Question 6 of 6
6. Question
Graph `x2y4=0`Hint
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Slope Intercept Form: `y=``m``x+``b`
 `m` is the slope of the line
 `b` is the yintercept (where the line cuts the yaxis)
First, convert the equation to Slope Intercept Form.`x2y4` `=` `0` `x2y4` `x` `=` `0` `x` Subtract `x` from both sides `2y4` `=` `x` `2y4` `+4` `=` `x` `+4` Add `4` to both sides `2y` `=` `x+4` `2y` `=` `x4` Convert the sign `2y``divide2` `=` `(x4)``divide2` Divide both sides by `2` `y` `=` `1/2x2` Next, identify the slope and `y`intercept.For: `y=``1/2``x``2`The slope `(m)` is `1/2` and the yintercept `(b)` is `2`.Now, plot the `y`intercept `(2)`Use the slope `m=1/2` to plot the next point.The slope 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 rightNow we can graph the equation
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