Graph the following equation and identify
the -intercept.

Use the graphing tool on the right to graph the equation.

Question

Graph the following equation and identify the $$ y $$-intercept. $$ y=x+2 $$ Use the graphing tool on the right to graph the equation.

UpStudy AI · Accepted Answer

1. **Identify the slope-intercept form:**  
   The equation is in the form  
   $$
   y = mx + b
   $$  
   where $$ m $$ is the slope and $$ b $$ is the $$ y $$-intercept.

2. **Compare with the given equation:**  
   The given equation is  
   $$
   y = x + 2
   $$  
   Here, the coefficient of $$ x $$ is $$ 1 $$ (so $$ m = 1 $$) and the constant term is $$ 2 $$ (so $$ b = 2 $$).

3. **Determine the $$ y $$-intercept:**  
   By definition, the $$ y $$-intercept is the point where the graph crosses the $$ y $$-axis. This happens when $$ x = 0 $$.  
   Substitute $$ x = 0 $$ into the equation:  
   $$
   y = 0 + 2 = 2
   $$  
   Therefore, the $$ y $$-intercept is at the point $$(0, 2)$$.

4. **Graphing the equation:**  
   To graph the line, start at the $$ y $$-intercept $$(0, 2)$$.  
   Since the slope $$ m = 1 $$, for every $$ 1 $$ unit increase in $$ x $$, $$ y $$ increases by $$ 1 $$ unit.  
   Some additional points on the line can be found by:
   - When $$ x = 1 $$:  
     $$
     y = 1 + 2 = 3 \quad \Rightarrow \quad (1, 3)
     $$
   - When $$ x = -1 $$:  
     $$
     y = -1 + 2 = 1 \quad \Rightarrow \quad (-1, 1)
     $$

5. **Final Answer:**  
   The $$ y $$-intercept of the graph of $$ y = x + 2 $$ is  
   $$
   (0, 2)
   $$
The $$ y $$-intercept of the graph of $$ y = x + 2 $$ is at the point $$(0, 2)$$.

Graph the following equation and identify
the -intercept.

Use the graphing tool on the right to graph the equation.

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Graph the following equation and identify the -intercept. Use the graphing tool on the right to graph the equation.

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Graph the following equation and identify
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Use the graphing tool on the right to graph the equation.