1. **State the problem:** We are given the linear equation $y = -2x + 3$ and want to understand its properties and graph. 2. **Formula and rules:** 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 $m = -2$ means the line descends 2 units vertically for every 1 unit it moves horizontally to the right. The y-intercept $b = 3$ means the line crosses the y-axis at the point $(0,3)$. 4. **Find x-intercept:** Set $y=0$ to find where the line crosses the x-axis: $$0 = -2x + 3$$ $$2x = 3$$ $$x = \frac{3}{2} = 1.5$$ So the x-intercept is at $(1.5, 0)$. 5. **Summary:** The line passes through $(0,3)$ on the y-axis and $(1.5,0)$ on the x-axis, with a slope of $-2$ indicating it goes downwards from left to right. **Final answer:** The linear equation $y = -2x + 3$ has slope $-2$, y-intercept $(0,3)$, and x-intercept $(1.5,0)$.