To determine which equation represents a given line in slope-intercept form, we need to analyze the structure of the given equations and match them to the correct slope ([tex]\(m\)[/tex]) and y-intercept ([tex]\(b\)[/tex]). The slope-intercept form of a line is given by:
[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, which is the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex].
We need to check the provided equations to find the one that matches the given format [tex]\( y = mx + b \)[/tex].
1. Equation: [tex]\( y = -\frac{5}{3} x - 1 \)[/tex]
- Here, [tex]\( m = -\frac{5}{3} \)[/tex] and [tex]\( b = -1 \)[/tex].
- This means the slope of the line is [tex]\(-\frac{5}{3}\)[/tex] and the y-intercept is [tex]\(-1\)[/tex].
2. Equation: [tex]\( y = \frac{5}{3} x + 1 \)[/tex]
- Here, [tex]\( m = \frac{5}{3} \)[/tex] and [tex]\( b = 1 \)[/tex].
- This means the slope of the line is [tex]\(\frac{5}{3}\)[/tex] and the y-intercept is [tex]\(1\)[/tex].
3. Equation: [tex]\( y = \frac{3}{5} x + 1 \)[/tex]
- Here, [tex]\( m = \frac{3}{5} \)[/tex] and [tex]\( b = 1 \)[/tex].
- This means the slope of the line is [tex]\(\frac{3}{5}\)[/tex] and the y-intercept is [tex]\(1\)[/tex].
4. Equation: [tex]\( y = -\frac{3}{5} x - 1 \)[/tex]
- Here, [tex]\( m = -\frac{3}{5} \)[/tex] and [tex]\( b = -1 \)[/tex].
- This means the slope of the line is [tex]\(-\frac{3}{5}\)[/tex] and the y-intercept is [tex]\(-1\)[/tex].
Now, our goal is to choose the correct equation based on the given slope and y-intercept values.
Given the analysis:
- The slope is [tex]\(-\frac{5}{3}\)[/tex]
- The y-intercept is [tex]\(-1\)[/tex]
The equation that matches these values is:
[tex]\[
y = -\frac{5}{3} x - 1
\][/tex]
Therefore, the correct equation in slope-intercept form is:
[tex]\[
y = -\frac{5}{3} x - 1
\][/tex]
Thus, the correct answer is:
[tex]\[ 1 \][/tex]
