From the image provided, you have a problem asking to determine the equation of a line on a coordinate plane, in the slope-intercept form $y = mx + b$.

Let me analyze the graph and break this down step by step:

Steps to Find the Equation of the Line

1. Find the slope ($m$):

   • Slope is calculated as $m = \frac{\Delta y}{\Delta x}$ (rise over run).
   • From the graph, select two points on the line. For example:
     • Point 1: $(-4, -6)$
     • Point 2: $(0, -2)$
   • Calculate the slope: $m = \frac{-2 - (-6)}{0 - (-4)} = \frac{-2 + 6}{4} = \frac{4}{4} = 1$ So, the slope is $m = 1$.

2. Find the y-intercept ($b$):

   • The y-intercept is where the line crosses the y-axis ($x = 0$).
   • From the graph, the line crosses the y-axis at $(0, -2)$.
   • Thus, the y-intercept is $b = -2$.

3. Write the equation:

   • Using $y = mx + b$, substitute $m = 1$ and $b = -2$: $y = 1x - 2 \quad \text{or simply} \quad y = x - 2.$

Final Answer:

The equation of the line is: $y = x - 2$

Would you like me to explain any part of this in more detail or go over another example?

Relative Questions:

1. What does the slope of a line tell us about its steepness or direction?
2. How can you determine the slope if the graph isn’t clear and you only have two points?
3. Why is the y-intercept significant in understanding a line's equation?
4. How can you rewrite $y = mx + b$ into standard form?
5. What happens to the equation of a line if the slope becomes zero?

Tip:

Always double-check your chosen points for accuracy when calculating the slope to avoid errors in the equation!