https://r2.erweima.ai/mathbot/image/1726163035014otf41mwp.jpg

The problem in the image is asking to determine the **x-intercept** and **y-intercept** of the graph for the linear equation \( y = 2x + 3 \) and to sketch the graph.

### Step-by-step Solution:

1. **Y-intercept**: The y-intercept occurs where \( x = 0 \).
   
   Substitute \( x = 0 \) into the equation:
   \[
   y = 2(0) + 3 = 3
   \]
   So, the y-intercept is at \( (0, 3) \).

2. **X-intercept**: The x-intercept occurs where \( y = 0 \).

   Substitute \( y = 0 \) into the equation:
   \[
   0 = 2x + 3
   \]
   Solving for \( x \):
   \[
   2x = -3 \implies x = -\frac{3}{2}
   \]
   So, the x-intercept is at \( \left(-\frac{3}{2}, 0\right) \).

3. **Sketching the Graph**:
   - Plot the y-intercept at \( (0, 3) \).
   - Plot the x-intercept at \( \left(-\frac{3}{2}, 0\right) \).
   - Draw a straight line through these two points.

Would you like me to provide more details or a plot of this graph? Here are some related questions that might interest you:

1. How do you find the slope of a line from its equation?
2. How do you find the equation of a line given two points?
3. What is the general form of a linear equation?
4. How do you calculate the distance between two points on a graph?
5. What is the difference between slope-intercept form and standard form of a line?

**Tip:** Remember that the slope-intercept form \( y = mx + b \) is very helpful in quickly determining the slope and y-intercept of a line!

Determinar las intersecciones x y y de la gráfica de y = 2x + 3 y hacer el bosquejo de su gráfica.

Learn how to find the x-intercept and y-intercept of the linear equation y = 2x + 3 and sketch the graph. This guide covers fundamental concepts of graphing and intercepts, ideal for students in Grades 8-10.

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