1. **State the problem:** We are given the linear equation $4x + 5y = 20$ and its slope-intercept form $y = -\frac{4}{5}x + 1$. We need to understand the graph of this line and solve it by graphing. 2. **Rewrite the equation in slope-intercept form:** The equation is already given as $y = -\frac{4}{5}x + 1$, where the slope $m = -\frac{4}{5}$ and the y-intercept $b = 1$. 3. **Interpret the slope and y-intercept:** The slope $-\frac{4}{5}$ means for every increase of 5 units in $x$, $y$ decreases by 4 units. The y-intercept $1$ means the line crosses the y-axis at the point $(0,1)$. 4. **Find the x-intercept:** Set $y=0$ and solve for $x$: $$0 = -\frac{4}{5}x + 1$$ $$\frac{4}{5}x = 1$$ $$x = \frac{1}{\frac{4}{5}} = \frac{1 \times 5}{4} = \frac{5}{4} = 1.25$$ So the x-intercept is at $(1.25, 0)$. 5. **Graph description:** The graph is a straight line passing through $(0,1)$ and $(1.25,0)$ with a negative slope, slanting downwards from left to right. 6. **Solving by graphing:** Plot the points $(0,1)$ and $(1.25,0)$ on the coordinate plane and draw a straight line through them. This line represents all solutions $(x,y)$ to the equation $4x + 5y = 20$. **Final answer:** The line $y = -\frac{4}{5}x + 1$ has slope $-\frac{4}{5}$, y-intercept $1$, and x-intercept $1.25$. Its graph is a straight line crossing the y-axis at $(0,1)$ and the x-axis at $(1.25,0)$.