To identify the slope and [tex]\( y \)[/tex]-intercept of each linear function's equation, we can rewrite each equation in the standard form of a linear equation, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the [tex]\( y \)[/tex]-intercept.
Let's analyze each equation step-by-step:
1. Equation: [tex]\( y = 3x - 1 \)[/tex]
- This equation is already in the form [tex]\( y = mx + b \)[/tex].
- Here, the slope ([tex]\( m \)[/tex]) is 3, and the [tex]\( y \)[/tex]-intercept ([tex]\( b \)[/tex]) is -1.
- Therefore, the slope is 3 and the [tex]\( y \)[/tex]-intercept is -1.
2. Equation: [tex]\( x - 3 = y \)[/tex]
- To rewrite in the form [tex]\( y = mx + b \)[/tex], we rearrange it as [tex]\( y = x - 3 \)[/tex].
- Here, the slope ([tex]\( m \)[/tex]) is 1, and the [tex]\( y \)[/tex]-intercept ([tex]\( b \)[/tex]) is -3.
- Therefore, the slope is 1 and the [tex]\( y \)[/tex]-intercept is -3.
3. Equation: [tex]\( -x + 3 = y \)[/tex]
- To rewrite in the form [tex]\( y = mx + b \)[/tex], we rearrange it as [tex]\( y = -x + 3 \)[/tex].
- Here, the slope ([tex]\( m \)[/tex]) is -1, and the [tex]\( y \)[/tex]-intercept ([tex]\( b \)[/tex]) is 3.
- Therefore, the slope is -1 and the [tex]\( y \)[/tex]-intercept is 3.
4. Equation: [tex]\( y = 1 - 3x \)[/tex]
- To rewrite in the form [tex]\( y = mx + b \)[/tex], we can rearrange it as [tex]\( y = -3x + 1 \)[/tex].
- Here, the slope ([tex]\( m \)[/tex]) is -3, and the [tex]\( y \)[/tex]-intercept ([tex]\( b \)[/tex]) is 1.
- Therefore, the slope is -3 and the [tex]\( y \)[/tex]-intercept is 1.
Summarizing the findings:
1. For [tex]\( y = 3x - 1 \)[/tex]:
- Slope = 3
- [tex]\( y \)[/tex]-intercept = -1
2. For [tex]\( x - 3 = y \)[/tex]:
- Slope = 1
- [tex]\( y \)[/tex]-intercept = -3
3. For [tex]\( -x + 3 = y \)[/tex]:
- Slope = -1
- [tex]\( y \)[/tex]-intercept = 3
4. For [tex]\( y = 1 - 3x \)[/tex]:
- Slope = -3
- [tex]\( y \)[/tex]-intercept = 1
This concludes the identification of the slopes and [tex]\( y \)[/tex]-intercepts for each given equation.
