We are given that the graph of the linear function $k$ passes through the points $(-7, 0)$ and $(1, 8)$.

Step 1: Check the x-intercept

The x-intercept is the point where the function crosses the x-axis, meaning the y-coordinate is 0. Since the point $(-7, 0)$ is given, this is the x-intercept. Thus:

• C: The x-intercept of the graph of k is $-7$ must be true.

Step 2: Find the slope

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

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

Using the points $(-7, 0)$ and $(1, 8)$:

$m = \frac{8 - 0}{1 - (-7)} = \frac{8}{1 + 7} = \frac{8}{8} = 1$

So, the slope is 1, not $-43$, which means D is false.

Step 3: Evaluate other options

• A: The zero of $k$ is 7 is false because the zero (x-intercept) is already determined to be $-7$, not 7.
• B: The graph of $k$ passes through the point $(-1, -8)$ is false. With a slope of 1 and passing through the x-intercept at $(-7, 0)$, we can calculate the equation of the line to verify this.

Step 4: Write the equation of the line

Using the point-slope form of a line $y - y_1 = m(x - x_1)$, where $m = 1$ and a point on the line is $(-7, 0)$:

$y - 0 = 1(x - (-7)) \implies y = x + 7$

Substitute $x = -1$ to check if the line passes through $(-1, -8)$:

$y = (-1) + 7 = 6$

Since $y = 6$, not $-8$, B is false.

Conclusion:

The correct statement is C: The x-intercept of the graph of $k$ is $-7$.

Would you like further details or have any questions?

Here are five related questions:

1. How is the equation of a line derived from two points?
2. What is the significance of the slope in a linear function?
3. How can you determine the y-intercept from two points?
4. Why is the x-intercept important in understanding the graph of a line?
5. How would the equation change if the slope was negative?

Tip: To find the slope of a line between two points, always remember the formula $\frac{y_2 - y_1}{x_2 - x_1}$.