The point-slope form of a line is:

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

Where:

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

Here:

• $m = \frac{1}{2}$
• $(x_1, y_1) = (16, -16)$

Substitute these values into the formula:

$y - (-16) = \frac{1}{2}(x - 16)$

Simplify:

$y + 16 = \frac{1}{2}(x - 16)$

Distribute the $\frac{1}{2}$:

$y + 16 = \frac{1}{2}x - 8$

Subtract 16 from both sides to isolate $y$:

$y = \frac{1}{2}x - 8 - 16$

$y = \frac{1}{2}x - 24$

Final Answer:

The equation of the line in slope-intercept form is:

$y = \frac{1}{2}x - 24$

Alternatively, you can leave it in point-slope form:

$y + 16 = \frac{1}{2}(x - 16)$

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Would you like a deeper explanation or more examples?

Related Questions:

1. How do you convert between point-slope and slope-intercept forms?
2. What does the slope represent in a real-world scenario?
3. How do you find the slope given two points?
4. How can you determine if two lines are parallel or perpendicular?
5. How do you graph a line given in point-slope form?

Tip:

Always simplify the equation as much as possible when solving problems unless the form is specifically required!