Question

find the y-intercept of the line $y = 13x + 11$. write your answer as an integer or as a simplified proper or improper ordered pair.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. The $y$-intercept is the point where the line crosses the $y$-axis, and at this point, $x = 0$.

Step2: Identify the $y$-intercept from the equation

Given the equation $y=13x + 11$, comparing it with $y=mx + b$, we can see that $b = 11$. When $x = 0$, $y=b$. So the $y$-intercept as an ordered pair is $(0,11)$ and as a value (the $y$-coordinate when $x = 0$) is $11$. Since the question allows an integer or an ordered pair, and if we consider the $y$-intercept value (or the ordered pair $(0,11)$), but since it asks for an integer or a simplified ordered pair, the $y$-intercept (the value of $y$ when $x = 0$) is $11$ or the ordered pair is $(0,11)$.

Answer:

The $y$-intercept is $11$ (or the ordered pair $(0,11)$). If we write it as an integer (the $y$-coordinate of the $y$-intercept), the answer is $11$.