Sure, let's identify the slope and [tex]\( y \)[/tex]-intercept for each given linear function's equation.
1. First Linear Function:
- Slope: [tex]\( 1 \)[/tex]
- [tex]\( y \)[/tex]-Intercept: [tex]\( -3 \)[/tex]
So, the equation of the first line in slope-intercept form [tex]\( y = mx + b \)[/tex] is:
[tex]\[
y = 1x - 3 \quad \text{or simply} \quad y = x - 3
\][/tex]
2. Second Linear Function:
- Slope: [tex]\( -1 \)[/tex]
- [tex]\( y \)[/tex]-Intercept: [tex]\( 3 \)[/tex]
The equation of the second line is:
[tex]\[
y = -1x + 3 \quad \text{or} \quad y = -x + 3
\][/tex]
3. Third Linear Function:
- Slope: [tex]\( -3 \)[/tex]
- [tex]\( y \)[/tex]-Intercept: [tex]\( 1 \)[/tex]
The equation of the third line is:
[tex]\[
y = -3x + 1
\][/tex]
4. Fourth Linear Function:
- Slope: [tex]\( 3 \)[/tex]
- [tex]\( y \)[/tex]-Intercept: [tex]\( -1 \)[/tex]
Finally, the equation of the fourth line is:
[tex]\[
y = 3x - 1
\][/tex]
Thus, the slopes and [tex]\( y \)[/tex]-intercepts for each of the given linear functions are:
1. Slope: [tex]\( 1 \)[/tex]; [tex]\( y \)[/tex]-intercept: [tex]\(-3\)[/tex]
2. Slope: [tex]\( -1 \)[/tex]; [tex]\( y \)[/tex]-intercept: [tex]\( 3 \)[/tex]
3. Slope: [tex]\( -3 \)[/tex]; [tex]\( y \)[/tex]-intercept: [tex]\( 1 \)[/tex]
4. Slope: [tex]\( 3 \)[/tex]; [tex]\( y \)[/tex]-intercept: [tex]\( -1 \)[/tex]
