1. The problem is to graph the linear equation $4x + 5y = 20$ and understand its slope-intercept form. 2. The slope-intercept form of a line is given by $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. Starting with the equation $4x + 5y = 20$, solve for $y$: $$5y = 20 - 4x$$ $$y = \frac{20 - 4x}{5} = -\frac{4}{5}x + 4$$ 4. Here, the slope $m = -\frac{4}{5}$ and the y-intercept $b = 4$. 5. This means the line crosses the y-axis at $(0,4)$ and for every increase of 5 units in $x$, $y$ decreases by 4 units. 6. To graph, plot the y-intercept $(0,4)$, then use the slope to find another point: from $(0,4)$ move right 5 units to $x=5$ and down 4 units to $y=0$, giving point $(5,0)$. 7. Draw a straight line through these points to represent the equation. 8. The given form $y = -\frac{4}{5}x + 1$ is incorrect for this equation; the correct y-intercept is 4, not 1. Final answer: The correct slope-intercept form is $$y = -\frac{4}{5}x + 4$$ and the graph is a line crossing the y-axis at 4 with slope $-\frac{4}{5}$.