To find the equation of the line in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept, let's analyze the given graph.

1. Identify the y-intercept ($b$):

   • The graph shows that the line crosses the y-axis at $y = 1$. Therefore, $b = 1$.

2. Calculate the slope ($m$):

   • To find the slope, use two points on the line. Based on the grid, we can see that the line passes through the points $(0, 1)$ and $(1, -1)$.
   • The formula for slope is $m = \frac{y_2 - y_1}{x_2 - x_1}$.
   • Substituting the points $(0, 1)$ and $(1, -1)$: $m = \frac{-1 - 1}{1 - 0} = \frac{-2}{1} = -2$

3. Form the equation:

   • With $m = -2$ and $b = 1$, the equation of the line is: $y = -2x + 1$

Answer

The correct answer is: $y = -2x + 1$, which matches none of the options given. It appears the provided answer options may not include the correct solution based on this graph analysis.

Would you like more details or have any questions?

Further Questions for Practice

1. How do you determine the slope if the graph has no clear points?
2. What if the line was vertical or horizontal? How would the equation look?
3. Can you identify other forms of linear equations besides slope-intercept form?
4. How does changing the slope affect the steepness of the line on a graph?
5. What would the equation be if the y-intercept was 0?

Tip:

To quickly find the slope, use two points where the line crosses grid intersections, as these are usually easier to read accurately.