The point-slope form of a line equation is given as:

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

where:

• $m$ is the slope of the line,
• $(x_1, y_1)$ is a point on the line.

Here, the slope $m = \frac{1}{2}$, and the point is $(10, -8)$.

Substituting these values into the formula:

$y - (-8) = \frac{1}{2}(x - 10)$

Simplify:

$y + 8 = \frac{1}{2}(x - 10)$

Thus, the equation in point-slope form is:

$y + 8 = \frac{1}{2}(x - 10)$

Let me know if you'd like further clarification or additional steps!

Related Questions:

1. How can you rewrite this equation in slope-intercept form?
2. What is the y-intercept of this line based on this equation?
3. How would the equation change if the slope were $-\frac{1}{2}$?
4. How do you graph a line given in point-slope form?
5. Can you derive the standard form of this line equation?

Tip:

When working with point-slope form, always ensure you correctly identify the slope and the coordinates of the point before substituting into the formula!