The problem is to graph the linear equation $4x + 7y = -7$.

1. Problem Description

The problem is to graph the linear equation $4x + 7y = -7$.

2. Solution Steps

To graph the equation $4x + 7y = -7$, we can find two points on the line and then draw the line through those points. We can find the intercepts.

To find the $x$-intercept, set $y = 0$ and solve for $x$:

$4x + 7(0) = -7$

$4x = -7$

$x = -\frac{7}{4}$

So, the $x$-intercept is $(-\frac{7}{4}, 0)$ or $(-1.75, 0)$.

To find the $y$-intercept, set $x = 0$ and solve for $y$:

$4(0) + 7y = -7$

$7y = -7$

$y = -1$

So, the $y$-intercept is $(0, -1)$.

We can plot the points $(-1.75, 0)$ and $(0, -1)$ on the graph and draw a line through them.

Alternatively, we can rearrange the equation to slope-intercept form: $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.

$4x + 7y = -7$

$7y = -4x - 7$

$y = -\frac{4}{7}x - 1$

The $y$-intercept is $-1$, which means the line passes through $(0, -1)$. The slope is $-\frac{4}{7}$. This means that for every 7 units we move to the right, we move 4 units down. So, starting from $(0, -1)$, we can move 7 units to the right and 4 units down to reach the point $(7, -5)$.

3. Final Answer

$y = -\frac{4}{7}x - 1$