To determine the equation for the given line in slope-intercept form, let's analyze each provided equation by identifying and comparing its slope and y-intercept.
Given multiple choice equations are:
1. [tex]\( y = -\frac{5}{3}x - 1 \)[/tex]
2. [tex]\( y = \frac{5}{3}x + 1 \)[/tex]
3. [tex]\( y = \frac{3}{5}x + 1 \)[/tex]
4. [tex]\( y = -\frac{3}{5}x - 1 \)[/tex]
In the slope-intercept form of a line equation, [tex]\( y = mx + c \)[/tex], "m" represents the slope, and "c" represents the y-intercept.
Let's list down the slopes and y-intercepts for all the given equations:
1. [tex]\( y = -\frac{5}{3}x - 1 \)[/tex]
- Slope ([tex]\(m\)[/tex]): [tex]\( -\frac{5}{3} \)[/tex]
- Y-intercept ([tex]\(c\)[/tex]): [tex]\( -1 \)[/tex]
2. [tex]\( y = \frac{5}{3}x + 1 \)[/tex]
- Slope ([tex]\(m\)[/tex]): [tex]\( \frac{5}{3} \)[/tex]
- Y-intercept ([tex]\(c\)[/tex]): [tex]\( 1 \)[/tex]
3. [tex]\( y = \frac{3}{5}x + 1 \)[/tex]
- Slope ([tex]\(m\)[/tex]): [tex]\( \frac{3}{5} \)[/tex]
- Y-intercept ([tex]\(c\)[/tex]): [tex]\( 1 \)[/tex]
4. [tex]\( y = -\frac{3}{5}x - 1 \)[/tex]
- Slope ([tex]\(m\)[/tex]): [tex]\( -\frac{3}{5} \)[/tex]
- Y-intercept ([tex]\(c\)[/tex]): [tex]\( -1 \)[/tex]
Now we compile this information as follows:
- (-1.6666666666666667, -1)
- (1.6666666666666667, 1)
- (0.6, 1)
- (-0.6, -1)
These calculated values match the values in the options exactly as follows:
1. [tex]\(y = -\frac{5}{3}x - 1 \)[/tex] corresponds to (-1.6666666666666667, -1)
2. [tex]\(y = \frac{5}{3}x + 1 \)[/tex] corresponds to (1.6666666666666667, 1)
3. [tex]\(y = \frac{3}{5}x + 1 \)[/tex] corresponds to (0.6, 1)
4. [tex]\(y = -\frac{3}{5}x - 1 \)[/tex] corresponds to (-0.6, -1)
Thus, with the detailed comparison, we confirm the corresponding representations for each equation in slope-intercept form:
1. [tex]\( y = -\frac{5}{3}x - 1 \)[/tex] = (-1.6666666666666667, -1)
2. [tex]\( y = \frac{5}{3}x + 1 \)[/tex] = (1.6666666666666667, 1)
3. [tex]\( y = \frac{3}{5}x + 1 \)[/tex] = (0.6, 1)
4. [tex]\( y = -\frac{3}{5}x - 1 \)[/tex] = (-0.6, -1)
So, the provided equations and their respective coefficients match the calculated results exactly.
