To identify the given equation of a line, we first need to recognize the structure of a linear equation in slope-intercept form, which is given as:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept of the line.
Now, let's analyze each of the provided equations to determine their slopes ([tex]\( m \)[/tex]) and y-intercepts ([tex]\( b \)[/tex]).
1. Equation: [tex]\( y = -\frac{5}{3}x - 1 \)[/tex]
- Slope ( [tex]\( m \)[/tex] ): [tex]\(-\frac{5}{3}\)[/tex] (approximately [tex]\(-1.6667\)[/tex])
- Y-intercept ( [tex]\( b \)[/tex] ): [tex]\(-1\)[/tex]
2. Equation: [tex]\( y = 8x + 1 \)[/tex]
- Slope ( [tex]\( m \)[/tex] ): [tex]\(8\)[/tex]
- Y-intercept ( [tex]\( b \)[/tex] ): [tex]\(1\)[/tex]
3. Equation: [tex]\( y = \frac{3}{5}x + 1 \)[/tex]
- Slope ( [tex]\( m \)[/tex] ): [tex]\(\frac{3}{5}\)[/tex] (approximately [tex]\(0.6\)[/tex])
- Y-intercept ( [tex]\( b \)[/tex] ): [tex]\(1\)[/tex]
4. Equation: [tex]\( y = -3x - 1 \)[/tex]
- Slope ( [tex]\( m \)[/tex] ): [tex]\(-3\)[/tex]
- Y-intercept ( [tex]\( b \)[/tex] ): [tex]\(-1\)[/tex]
After identifying the slopes and y-intercepts of each equation, we can summarize the results for each equation:
1. [tex]\( y = -\frac{5}{3}x - 1 \)[/tex]:
- Slope = [tex]\(-1.6667\)[/tex]
- Y-intercept = [tex]\(-1\)[/tex]
2. [tex]\( y = 8x + 1 \)[/tex]:
- Slope = [tex]\(8\)[/tex]
- Y-intercept = [tex]\(1\)[/tex]
3. [tex]\( y = \frac{3}{5}x + 1 \)[/tex]:
- Slope = [tex]\(0.6\)[/tex]
- Y-intercept = [tex]\(1\)[/tex]
4. [tex]\( y = -3x - 1 \)[/tex]:
- Slope = [tex]\(-3\)[/tex]
- Y-intercept = [tex]\(-1\)[/tex]
Thus, all the equations have been correctly analyzed for their slope and intercept in the slope-intercept form.
