graph the line $$ 2 x+5 y=-10 $$

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To graph the line given by the equation $$ 2x + 5y = -10 $$, we can follow these steps:

1. **Convert to Slope-Intercept Form**: We can rearrange the equation into the form $$ y = mx + b $$, where $$ m $$ is the slope and $$ b $$ is the y-intercept.

Starting with the original equation:
   $$
   2x + 5y = -10
   $$
   Subtract $$ 2x $$ from both sides:
   $$
   5y = -2x - 10
   $$
   Now, divide every term by 5:
   $$
   y = -\frac{2}{5}x - 2
   $$

Here, the slope $$ m = -\frac{2}{5} $$ and the y-intercept $$ b = -2 $$.

2. **Plot the Y-Intercept**: The y-intercept is the point where the line crosses the y-axis. This occurs at $$ (0, -2) $$.

3. **Use the Slope to Find Another Point**: The slope $$ -\frac{2}{5} $$ means that for every 5 units you move to the right (positive x-direction), you move down 2 units (negative y-direction). Starting from the y-intercept $$ (0, -2) $$:
   - Move 5 units to the right to $$ (5, -2) $$.
   - Move down 2 units to $$ (5, -4) $$.

So, another point on the line is $$ (5, -4) $$.

4. **Plot the Points and Draw the Line**: Now, plot the points $$ (0, -2) $$ and $$ (5, -4) $$ on a coordinate plane. Draw a straight line through these points, extending it in both directions.

5. **Label the Line**: Optionally, you can label the line with its equation $$ 2x + 5y = -10 $$.

This is how you would graph the line. If you have graphing software or graph paper, you can plot these points and draw the line accordingly.
To graph $$ 2x + 5y = -10 $$, rearrange to $$ y = -\frac{2}{5}x - 2 $$. Plot the y-intercept (0, -2) and use the slope (-2/5) to find another point like (5, -4). Draw a line through these points.

graph the line

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