1. **State the problem:** We are given the linear function $y = -2x + 3$ and want to understand its properties. 2. **Formula and explanation:** This is a linear equation in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Identify slope and intercept:** Here, the slope $m = -2$ and the y-intercept $b = 3$. 4. **Find x-intercept:** Set $y=0$ and solve for $x$: $$0 = -2x + 3$$ $$2x = 3$$ $$x = \frac{3}{2}$$ 5. **Interpretation:** The line crosses the y-axis at $(0,3)$ and the x-axis at $\left(\frac{3}{2}, 0\right)$. 6. **Slope meaning:** The slope $-2$ means for every 1 unit increase in $x$, $y$ decreases by 2 units. 7. **Summary:** The function is a straight line with negative slope, intercepting y-axis at 3 and x-axis at $1.5$.