To solve the problem, we need to create the equation of a line in slope-intercept form, $y = mx + b$, using the data from the table of $x$- and $y$-values.

Step 1: Calculate the slope ($m$)

The slope $m$ can be calculated using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Choose any two points from the table. For example, use the points $(-4, -1)$ and $(4, 5)$: $m = \frac{5 - (-1)}{4 - (-4)} = \frac{5 + 1}{4 + 4} = \frac{6}{8} = \frac{3}{4}$ So, $m = \frac{3}{4}$.

Step 2: Solve for the $y$-intercept ($b$)

Substitute one point and the slope into the slope-intercept form, $y = mx + b$. Using the point $(-4, -1)$: $-1 = \frac{3}{4}(-4) + b$ $-1 = -3 + b$ $b = -1 + 3 = 2$

Step 3: Write the equation

The equation is: $y = \frac{3}{4}x + 2$

Final Answer:

• Slope ($m$): $\frac{3}{4}$
• Intercept ($b$): $2$

Let me know if you'd like additional clarification or further assistance!

Related Questions:

1. How is slope calculated between two points?
2. What does the slope represent in the context of a linear equation?
3. How can you determine if two points lie on the same line?
4. How do you verify that a given equation matches a set of points?
5. What are other forms of linear equations besides slope-intercept form?

Tip: Always simplify the slope fraction, if possible, to its lowest terms to make calculations clearer.