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Identify the slope and [tex]$y$[/tex]-intercept of each linear function's equation.

1. [tex]\( y = 3x - 1 \)[/tex]
2. [tex]\( x - 3 = y \)[/tex]
3. [tex]\( -x + 3 = y \)[/tex]
4. [tex]\( y = 1 - 3x \)[/tex]

a. Slope: [tex]\( -3 \)[/tex], [tex]\( y \)[/tex]-intercept: 1
b. Slope: 1, [tex]\( y \)[/tex]-intercept: -3
c. Slope: 3, [tex]\( y \)[/tex]-intercept: -1

Sagot :

GinnyAnsweridn
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.
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