To solve for the slope and y-intercept of the linear function passing through the points $(-7, -4)$ and $(7, 6)$, let's follow these steps:

Step 1: Find the Slope

The formula for the slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the given points $(-7, -4)$ and $(7, 6)$:

$m = \frac{6 - (-4)}{7 - (-7)} = \frac{6 + 4}{7 + 7} = \frac{10}{14} = \frac{5}{7}$

So, the slope $m$ is $\frac{5}{7}$.

Step 2: Find the Y-intercept

The equation of a line in slope-intercept form is:

$y = mx + b$

Where $m$ is the slope and $b$ is the y-intercept. We can use one of the points and the slope to solve for $b$.

Using the point $(-7, -4)$:

$-4 = \frac{5}{7}(-7) + b$

Simplify and solve for $b$:

$-4 = -5 + b \implies b = -4 + 5 = 1$

So, the y-intercept $b$ is $1$.

Conclusion

The correct answer is: B. The slope is $\frac{5}{7}$, and the y-intercept is 1.

Would you like further details or have any questions?

Here are 5 related questions:

1. How would you find the equation of the line given a different set of points?
2. Can you explain why the slope formula works?
3. How do you convert between different forms of a linear equation?
4. What does the slope represent in a real-world context?
5. How can you graph a line using its slope and y-intercept?

Tip: Remember that the y-intercept is where the line crosses the y-axis, which means $x = 0$ at that point.