Let's find the slope and [tex]\(y\)[/tex]-intercept for each of the given equations step by step.
### (a) [tex]\( x - 8y - 24 = 0 \)[/tex]
1. Rewrite the equation in slope-intercept form [tex]\(y = mx + b\)[/tex]:
[tex]\[ x - 8y - 24 = 0 \][/tex]
[tex]\[ -8y = -x + 24 \][/tex]
[tex]\[ y = \frac{1}{8}x - 3 \][/tex]
2. Identify the slope (m) and [tex]\(y\)[/tex]-intercept (b):
- Slope, [tex]\( m = \frac{1}{8} \)[/tex]
- [tex]\( y \)[/tex]-intercept, [tex]\( b = -3 \)[/tex]
### (b) [tex]\( y = \sqrt{3} x + 3 \)[/tex]
1. This equation is already in slope-intercept form [tex]\(y = mx + b\)[/tex]:
[tex]\[ y = \sqrt{3} x + 3 \][/tex]
2. Identify the slope (m) and [tex]\(y\)[/tex]-intercept (b):
- Slope, [tex]\( m = \sqrt{3} \approx 1.732 \)[/tex]
- [tex]\( y \)[/tex]-intercept, [tex]\( b = 3 \)[/tex]
### (c) [tex]\( y = 4x + 8 \)[/tex]
1. This equation is also already in slope-intercept form [tex]\(y = mx + b\)[/tex]:
[tex]\[ y = 4x + 8 \][/tex]
2. Identify the slope (m) and [tex]\(y\)[/tex]-intercept (b):
- Slope, [tex]\( m = 4 \)[/tex]
- [tex]\( y \)[/tex]-intercept, [tex]\( b = 8 \)[/tex]
### Conclusion:
- For equation (a) [tex]\(x - 8y - 24 = 0\)[/tex]:
- Slope, [tex]\(m = \frac{1}{8} = 0.125\)[/tex]
- [tex]\(y\)[/tex]-intercept, [tex]\(b = -3\)[/tex]
- For equation (b) [tex]\( y = \sqrt{3} x + 3 \)[/tex]:
- Slope, [tex]\(m = \sqrt{3} = 1.732\)[/tex]
- [tex]\(y\)[/tex]-intercept, [tex]\(b = 3\)[/tex]
- For equation (c) [tex]\( y = 4x + 8 \)[/tex]:
- Slope, [tex]\(m = 4\)[/tex]
- [tex]\(y\)[/tex]-intercept, [tex]\(b = 8\)[/tex]
