To determine the equation for the given line in slope-intercept form, let's analyze the options provided.
The slope-intercept form of a line is given by:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] represents the slope of the line, and [tex]\( b \)[/tex] is the y-intercept (the value of y when x = 0).
Let's consider the possible equations one by one:
1. [tex]\( y = -\frac{5}{3} x - 1 \)[/tex]
- Here, the slope [tex]\( m \)[/tex] is [tex]\(-\frac{5}{3}\)[/tex] and the y-intercept [tex]\( b \)[/tex] is [tex]\(-1\)[/tex].
2. [tex]\( y = \frac{5}{3} x + 1 \)[/tex]
- Here, the slope [tex]\( m \)[/tex] is [tex]\(\frac{5}{3}\)[/tex] and the y-intercept [tex]\( b \)[/tex] is [tex]\(1\)[/tex].
3. [tex]\( y = \frac{3}{5} x + 1 \)[/tex]
- Here, the slope [tex]\( m \)[/tex] is [tex]\(\frac{3}{5}\)[/tex] and the y-intercept [tex]\( b \)[/tex] is [tex]\(1\)[/tex].
4. [tex]\( y = -\frac{3}{5} x - 1 \)[/tex]
- Here, the slope [tex]\( m \)[/tex] is [tex]\(-\frac{3}{5}\)[/tex] and the y-intercept [tex]\( b \)[/tex] is [tex]\(-1\)[/tex].
Out of these options, the correct line equation is:
[tex]\[
y = \frac{3}{5} x + 1
\][/tex]
So, the equation in slope-intercept form is [tex]\( y = \frac{3}{5} x + 1 \)[/tex].
