1. **State the problem:** We are given the linear equation $y = -4x + 5$ and need to understand its graph and key features. 2. **Formula and rules:** This is a linear function in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Identify slope and intercept:** Here, $m = -4$ and $b = 5$. The slope $-4$ means the line falls 4 units vertically for every 1 unit it moves horizontally to the right. 4. **Find the y-intercept:** The y-intercept is the point where $x=0$, so $y = 5$. This gives the point $(0,5)$. 5. **Find the x-intercept:** Set $y=0$ and solve for $x$: $$ 0 = -4x + 5 $$ $$ 4x = 5 $$ $$ x = \frac{5}{4} $$ So the x-intercept is at $\left(\frac{5}{4}, 0\right)$. 6. **Plot points and draw the line:** Plot $(0,5)$ and $\left(\frac{5}{4}, 0\right)$ on the coordinate plane and draw a straight line through them. 7. **Summary:** The line crosses the y-axis at 5 and the x-axis at $\frac{5}{4}$, with a negative slope indicating it decreases from left to right.