The problem asks to graph the linear equation $3x + 5y = -5$.

1. Problem Description

The problem asks to graph the linear equation $3x + 5y = -5$.

2. Solution Steps

To graph the equation $3x + 5y = -5$, we can find two points on the line and then connect them. A good approach is to find the x and y intercepts.

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

$3x + 5(0) = -5$

$3x = -5$

$x = -\frac{5}{3}$

So, the x-intercept is $(-\frac{5}{3}, 0)$.

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

$3(0) + 5y = -5$

$5y = -5$

$y = -1$

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

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

$3x + 5y = -5$

$5y = -3x - 5$

$y = -\frac{3}{5}x - 1$

From this form, we can see that the slope is $-\frac{3}{5}$ and the y-intercept is $-1$. This matches with our previous calculation.

We have two points: $(-\frac{5}{3}, 0)$ and $(0, -1)$. We can now graph the line. Since we do not have the tool, the solution is just finding the two points. We can also find another point using the slope-intercept form. For example, starting from (0,-1), we move 5 units to the right and 3 units down. This leads to the point (5, -4).

3. Final Answer

Two points on the line are $(-\frac{5}{3}, 0)$ and $(0, -1)$. The slope-intercept form is $y = -\frac{3}{5}x - 1$.