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

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

For each equation, determine the following:
- Slope: [tex]\( m \)[/tex]
- [tex]\( y \)[/tex]-intercept: [tex]\( b \)[/tex]

Choices:
A. Slope [tex]\( = 3 \)[/tex]; [tex]\( y \)[/tex]-intercept at [tex]\(-1\)[/tex]
B. Slope [tex]\( = -1 \)[/tex]; [tex]\( y \)[/tex]-intercept at [tex]\( 3 \)[/tex]
C. Slope [tex]\( = -3 \)[/tex]; [tex]\( y \)[/tex]-intercept at [tex]\( 1 \)[/tex]
D. Slope [tex]\( = 1 \)[/tex]; [tex]\( y \)[/tex]-intercept at [tex]\(-3\)[/tex]



Answer :

GinnyAnswer
Sure, let's go through each linear function's equation to identify its slope and [tex]\( y \)[/tex]-intercept.

### 1. Equation: [tex]\( x - 3 = y \)[/tex]

To express this in the form [tex]\( y = mx + c \)[/tex] where [tex]\( m \)[/tex] is the slope and [tex]\( c \)[/tex] is the [tex]\( y \)[/tex]-intercept, we rearrange the equation:

[tex]\( x - 3 = y \)[/tex]

Let's rewrite it:

[tex]\( y = x - 3 \)[/tex]

Here, the slope [tex]\( m \)[/tex] is 1, and the [tex]\( y \)[/tex]-intercept [tex]\( c \)[/tex] is -3.

So, the slope is [tex]\( 1 \)[/tex] and the [tex]\( y \)[/tex]-intercept is [tex]\( -3 \)[/tex].

### 2. Equation: [tex]\( y = 3x - 1 \)[/tex]

This is already in the form [tex]\( y = mx + c \)[/tex].

Here, the slope [tex]\( m \)[/tex] is 3, and the [tex]\( y \)[/tex]-intercept [tex]\( c \)[/tex] is -1.

So, the slope is [tex]\( 3 \)[/tex] and the [tex]\( y \)[/tex]-intercept is [tex]\( -1 \)[/tex].

### 3. Equation: [tex]\( y = 1 - 3x \)[/tex]

To express this equation in the form [tex]\( y = mx + c \)[/tex], we rearrange the terms:

[tex]\[ y = 1 - 3x \][/tex]

We can rewrite it as:

[tex]\[ y = -3x + 1 \][/tex]

Here, the slope [tex]\( m \)[/tex] is -3, and the [tex]\( y \)[/tex]-intercept [tex]\( c \)[/tex] is 1.

So, the slope is [tex]\( -3 \)[/tex] and the [tex]\( y \)[/tex]-intercept is [tex]\( 1 \)[/tex].

### 4. Equation: [tex]\( -x + 3 = y \)[/tex]

To express this in the form [tex]\( y = mx + c \)[/tex], we rearrange the equation:

[tex]\[ -x + 3 = y \][/tex]

Let's rewrite it:

[tex]\[ y = -x + 3 \][/tex]

Here, the slope [tex]\( m \)[/tex] is -1, and the [tex]\( y \)[/tex]-intercept [tex]\( c \)[/tex] is 3.

So, the slope is [tex]\( -1 \)[/tex] and the [tex]\( y \)[/tex]-intercept is [tex]\( 3 \)[/tex].

### Summary:

- For the equation [tex]\( x - 3 = y \)[/tex]:
- Slope: [tex]\( 1 \)[/tex]
- [tex]\( y \)[/tex]-intercept: [tex]\( -3 \)[/tex]

- For the equation [tex]\( y = 3x - 1 \)[/tex]:
- Slope: [tex]\( 3 \)[/tex]
- [tex]\( y \)[/tex]-intercept: [tex]\( -1 \)[/tex]

- For the equation [tex]\( y = 1 - 3x \)[/tex]:
- Slope: [tex]\( -3 \)[/tex]
- [tex]\( y \)[/tex]-intercept: [tex]\( 1 \)[/tex]

- For the equation [tex]\( -x + 3 = y \)[/tex]:
- Slope: [tex]\( -1 \)[/tex]
- [tex]\( y \)[/tex]-intercept: [tex]\( 3 \)[/tex]

I hope this step-by-step solution helps!

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