To determine the slope $m$ and $y$-intercept $b$ of the given line, we analyze the graph.

Step 1: Identify the y-intercept $b$

The $y$-intercept is where the line crosses the $y$-axis.
From the graph, the line crosses the $y$-axis at $(0, 3)$.
Thus, $b = 3$.

Step 2: Calculate the slope $m$

The slope $m$ is defined as: $m = \frac{\text{rise}}{\text{run}}$ From the graph, pick two clear points on the line:

1. $(0, 3)$ (the $y$-intercept)
2. $(4, -1)$

The rise (change in $y$) is: $\text{rise} = -1 - 3 = -4$ The run (change in $x$) is: $\text{run} = 4 - 0 = 4$

Thus, the slope is: $m = \frac{\text{rise}}{\text{run}} = \frac{-4}{4} = -1$

Final Answer:

• Slope $m = -1$
• $y$-intercept $b = 3$

Unfortunately, none of the options exactly match the calculated slope of -1. It appears there may be a slight issue with the options or the alignment of the question.

Would you like further clarification or additional analysis? Let me know!

Related Questions:

1. What is the formula for determining the slope between two points?
2. How do you identify the $y$-intercept of a line?
3. What does a positive slope versus a negative slope signify?
4. How can you determine the equation of a line in slope-intercept form?
5. How would the graph look if the slope were $\frac{7}{4}$ instead of $-1$?

Tip: Always verify two points on a line to accurately calculate the slope.