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Sagot :
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!
### 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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