Certainly! Let's go through the steps to convert the given equation from Standard Form to Slope-Intercept Form and then answer the questions about the slope and the y-intercept.
### Given Equation in Standard Form:
[tex]\[ 12x - 4y = 8 \][/tex]
### Steps to convert to Slope-Intercept Form ([tex]\(y = mx + b\)[/tex]):
1. Subtract [tex]\(12x\)[/tex] from both sides to isolate the [tex]\(y\)[/tex] term on one side:
[tex]\[ -4y = -12x + 8 \][/tex]
2. Divide both sides by [tex]\(-4\)[/tex] to solve for [tex]\(y\)[/tex]:
[tex]\[ y = \frac{-12x + 8}{-4} \][/tex]
3. Simplify the right-hand side:
[tex]\[ y = 3x - 2 \][/tex]
### Equation in Slope-Intercept Form:
[tex]\[ y = 3x - 2 \][/tex]
### Answering the Questions:
- The slope ([tex]\(m\)[/tex]) is:
[tex]\[ 3 \][/tex]
- The [tex]\(y\)[/tex]-intercept ([tex]\(b\)[/tex]) is:
[tex]\[ -2 \][/tex]
### Final Submission:
1. Start with the equation in Standard Form: [tex]\( 12x - 4y = 8 \)[/tex]
2. Subtract [tex]\( 12x \)[/tex] from both sides: [tex]\( -4y = -12x + 8 \)[/tex]
3. Divide both sides by [tex]\(-4\)[/tex]: [tex]\( y = 3x - 2 \)[/tex]
4. Result in Slope-Intercept Form: [tex]\( y = 3x - 2 \)[/tex]
- The slope is: [tex]\( 3 \)[/tex]
- The [tex]\( y \)[/tex]-intercept is: [tex]\( -2 \)[/tex]
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