Certainly! To find the [tex]$y$[/tex]-intercept of the given line represented by the equation:
[tex]\[
y = \frac{7}{10} x + \frac{11}{6}
\][/tex]
we need to determine the value of \( y \) when \( x = 0 \). The [tex]$y$[/tex]-intercept occurs at the point where the line crosses the y-axis, which is precisely when \( x = 0 \).
Here's the step-by-step process:
1. Set \( x \) to 0 in the equation:
[tex]\[
y = \frac{7}{10} \cdot 0 + \frac{11}{6}
\][/tex]
2. Simplify the equation:
[tex]\[
y = 0 + \frac{11}{6}
\][/tex]
3. Since \( 0 \) added to any number is the number itself, we get:
[tex]\[
y = \frac{11}{6}
\][/tex]
Thus, the [tex]$y$[/tex]-intercept of the line is:
[tex]\[
\boxed{1.8333333333333333}
\][/tex]
So, when rounded to a more manageable form, the [tex]$y$[/tex]-intercept is approximately 1.8333.
