To solve this problem, we need to determine both the slope and the y-intercept of the linear function $g$ that passes through the points $(-4, 4)$ and $(4, 6)$.

Step 1: Calculate the Slope

The slope $m$ of a line that passes through two points $(x_1, y_1)$ and $(x_2, y_2)$ can be calculated using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the given points:

• $(x_1, y_1) = (-4, 4)$
• $(x_2, y_2) = (4, 6)$

$m = \frac{6 - 4}{4 - (-4)} = \frac{2}{8} = \frac{1}{4}$

So, the slope $m = \frac{1}{4}$.

Step 2: Calculate the Y-Intercept

To find the y-intercept $b$, we can use the point-slope form of the line: $y = mx + b$ Substituting $m = \frac{1}{4}$ and using one of the points, say $(-4, 4)$: $4 = \frac{1}{4}(-4) + b$ $4 = -1 + b$ $b = 5$

Conclusion

The slope is $\frac{1}{4}$ and the y-intercept is $5$.

Answer

The correct choice is:

• The slope is $\frac{1}{4}$ and the y-intercept is $5$.

Would you like more details or have any questions?

Here are five related questions to deepen your understanding:

1. How would the graph change if the slope were negative?
2. How can you find the x-intercept of a line given its equation?
3. What is the general equation of a line in slope-intercept form?
4. How does the slope affect the steepness of a line?
5. Can you find the slope of a vertical or horizontal line?

Tip: When finding the slope between two points, make sure to consistently use $(x_1, y_1)$ and $(x_2, y_2)$ in the same order to avoid sign errors.