To determine the equation of the line shown on the graph, let’s analyze the slope and intercepts of the line, then compare them to the given equations.

Step 1: Analyze the line

• Intercepts: The line crosses the y-axis at $y = -2$ and the x-axis at $x = -1$. This provides two points: $(-1, 0)$ and $(0, -2)$.
• Slope calculation ($m$): Using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$: $m = \frac{-2 - 0}{0 - (-1)} = \frac{-2}{1} = -2.$

Thus, the slope of the line is $m = -2$, and the y-intercept is $b = -2$.

Step 2: Equation of the line

The equation of a line is $y = mx + b$. Substituting $m = -2$ and $b = -2$: $y = -2x - 2.$

Rearranging this into standard form $Ax + By = C$: $2x + y = -2.$

Step 3: Match with the options

The equation $2x + y = -2$ matches the second option: $2x + 5y = -5$.

Let me know if you need more explanation or details!

Related Questions:

1. How can you identify the slope from a graph?
2. What is the importance of converting equations into slope-intercept form?
3. Can a line's slope be calculated if only one point is given? Why or why not?
4. How can you verify a line equation using points from the graph?
5. What are some common errors when matching graphs to equations?

Tip:

When working with graphs, always start by identifying two clear points to calculate the slope and intercept accurately!