The given equation is:

$y = 2x + 3$

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

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

1. Identify the slope and y-intercept:

From $y = 2x + 3$:

• Slope ($m$) = $2$,
• Y-intercept ($b$) = $3$.

This means the line crosses the y-axis at $(0, 3)$.

2. Find the x-intercept:

To find the x-intercept, set $y = 0$ and solve for $x$:

$0 = 2x + 3$ $2x = -3 \quad \implies \quad x = -\frac{3}{2}$

Thus, the x-intercept is $\left( -\frac{3}{2}, 0 \right)$.

Final Answers:

• X-intercept: $\left( -\frac{3}{2}, 0 \right)$ or $(-1.5, 0)$,
• Y-intercept: $(0, 3)$,
• Slope: $2$.

If you'd like help graphing or further explanations, let me know!

5 Related Questions:

1. How do you determine the slope and intercepts of a linear equation in slope-intercept form?
2. What happens to the graph of $y = 2x + 3$ if the slope changes to $-2$?
3. How do you convert $y = 2x + 3$ to standard form $Ax + By = C$?
4. What is the general impact of the y-intercept on the graph of a line?
5. How do you find the intercepts for $y = -\frac{1}{2}x + 4$?

Tip: The slope $m$ represents the steepness of the line. A positive $m$ means the line rises as you move to the right!