The correct statement from the given options is:

For any value of Δx measured away from the point (0, −8) in the relationship, Δy = 5Δx.

Here’s why:

• The equation given is $y = 5x - 8$, which is in slope-intercept form, where the slope $m = 5$ and the y-intercept is $b = -8$.
• The slope $m = 5$ tells us that for every change in $x$, the corresponding change in $y$ is 5 times that of $x$.
• In other words, for any horizontal change $\Delta x$, the vertical change $\Delta y$ is $5 \times \Delta x$, which is exactly what the fourth statement says.

Breaking down other options:

1. The point (6, 22) in the relationship conveys that $6 = 5(22) - 8$:
   This statement is incorrect. If you substitute $x = 6$ into the equation $y = 5x - 8$, it should give you $y = 5(6) - 8 = 30 - 8 = 22$, which is correct. However, this statement does not match the form of the equation or make sense in its context.

2. Given any point $(x, y)$, $y$ is always 5 times as large as $x$:
   This is incorrect. The equation $y = 5x - 8$ means that $y$ is 5 times $x$, but offset by 8 (the y-intercept). It does not say that $y$ is exactly 5 times $x$.

3. Given any two points $(x_1, y_1)$ and $(x_2, y_2)$, $\frac{y_2 - y_1}{x_2 - x_1} = 5$:
   This is correct! It states the slope formula, and since the slope is 5 (from $y = 5x - 8$), this equation holds true for any two points on the line.

4. The point (6, 22) in the relationship conveys that $22 = 5(6) - 8$:
   This is correct! If you substitute $x = 6$, you get $y = 5(6) - 8 = 30 - 8 = 22$, which matches the point given.

Summary:

The statements about the slope $\frac{y_2 - y_1}{x_2 - x_1} = 5$ and the change in $y$ for a change in $x$ being 5 times the change in $x$ (i.e., $\Delta y = 5 \Delta x$) are accurate based on the given equation.

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Would you like more details on any of these concepts? Or would you like help with something else?

Here are some follow-up questions to explore related concepts:

1. How do you derive the slope from an equation in slope-intercept form?
2. What does the y-intercept represent in the equation of a line?
3. How can you graph the line represented by $y = 5x - 8$?
4. How do you find the slope between two points on a line?
5. What happens to the equation $y = 5x - 8$ if the slope changes to 3?

Tip: When interpreting a line’s equation, always check the slope (coefficient of $x$) and the y-intercept (constant term) to understand the line’s direction and position!