To solve the problem and determine the correct point-slope equation, we use the point-slope formula for a line:

$y - y_1 = m(x - x_1)$

Here:

• The point is $(4, -7)$, so $x_1 = 4$ and $y_1 = -7$,
• The slope is $m = -\frac{1}{4}$.

Substituting these values into the formula: $y - (-7) = -\frac{1}{4}(x - 4)$

Simplify: $y + 7 = -\frac{1}{4}(x - 4)$

Thus, the correct answer is:

$y + 7 = -\frac{1}{4}(x - 4)$

Let me know if you'd like further clarifications or have any questions!

5 Related Questions:

1. What does the slope $m = -1/4$ tell us about the line?
2. How do you convert point-slope form to slope-intercept form?
3. What happens if you change the slope $m$ to a positive value?
4. Can you write the equation in standard form instead of point-slope form?
5. How do you verify that the point $(4, -7)$ lies on the line?

Tip:

Always double-check the signs when using the point-slope formula, especially for negative values of $y_1$ or $x_1$.