The equation you provided, $y = 2x + 3$, represents a linear function. Let's analyze its key components:

1. Slope-Intercept Form

The equation is in slope-intercept form, $y = mx + b$, where:

• $m$ is the slope.
• $b$ is the y-intercept.

For $y = 2x + 3$:

• Slope (m): $2$
• Y-Intercept (b): $3$

2. Characteristics of the Line

• Slope: The slope of 2 means that for every 1 unit increase in $x$, the value of $y$ increases by 2 units.
• Y-Intercept: The line crosses the y-axis at the point $(0, 3)$.

3. Graphing the Line

To graph this equation:

1. Start by plotting the y-intercept (0, 3) on the coordinate plane.
2. Use the slope to find another point. Since the slope is 2, move up 2 units and 1 unit to the right from the y-intercept to get the next point, (1, 5).
3. Draw a straight line through these points.

4. Example Points on the Line

Here are a few points that satisfy the equation:

• $x = 0, y = 3$ (y-intercept)
• $x = 1, y = 5$
• $x = -1, y = 1$

Would you like a graph or further details?

Related Questions

1. How do you find the slope and y-intercept from any linear equation?
2. What is the meaning of a negative slope?
3. How do you convert a linear equation from slope-intercept to standard form?
4. How does changing the slope affect the graph of a line?
5. What are parallel and perpendicular lines?

Tip: Understanding how to interpret the slope and y-intercept helps in quickly graphing and analyzing linear equations.