b. What is the $$ y $$-intercept of the line for each equation? What does it mean in this context?

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1. An equation of a line is often written in slope-intercept form:  
   $$
   y = mx + b
   $$
   where $$ m $$ is the slope and $$ b $$ is the $$ y $$-intercept.

2. The $$ y $$-intercept is found by setting $$ x = 0 $$. When $$ x = 0 $$, the equation becomes:  
   $$
   y = m(0) + b = b
   $$
   Thus, the $$ y $$-intercept is $$ b $$, and it corresponds to the point $$ (0, b) $$ on the graph.

3. In this context, the $$ y $$-intercept $$ (0, b) $$ represents the value of $$ y $$ when the independent variable $$ x $$ is zero. Depending on the scenario being modeled, it often signifies the initial or starting amount of the quantity represented by $$ y $$ before any changes (as indicated by $$ x $$) occur.
The $$ y $$-intercept of a line is the point where the line crosses the $$ y $$-axis, which is when $$ x = 0 $$. It is represented by $$ b $$ in the equation $$ y = mx + b $$. In this context, the $$ y $$-intercept shows the value of $$ y $$ when $$ x $$ is zero, often indicating the starting amount before any changes occur.

b. What is the \( y \)-intercept of the line for each equation? What does it mean in this context?

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