To write the equation of the line in slope-intercept form (which is $y = mx + b$), we are given:

• A point on the line: $(-10, 6)$
• The slope of the line: $m = -\frac{1}{2}$

We can use the point-slope formula to find the equation of the line:

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

where $(x_1, y_1)$ is the point on the line and $m$ is the slope. Plugging in the values:

$y - 6 = -\frac{1}{2}(x + 10)$

Now, simplify the equation step by step:

$y - 6 = -\frac{1}{2}x - 5$

Next, solve for $y$:

$y = -\frac{1}{2}x - 5 + 6$ $y = -\frac{1}{2}x + 1$

So, the equation of the line in slope-intercept form is:

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

Would you like further explanation on any step, or details on how to solve other forms of line equations?

Here are some related questions to expand your understanding:

1. How can you convert a slope-intercept form equation to standard form?
2. What does the slope tell you about the direction of the line?
3. How would you determine the y-intercept given different points on the line?
4. Can the point-slope formula be used to find equations when the slope is undefined?
5. What happens to the slope-intercept form when the slope is 0?

Tip: The slope $m$ tells you how much the line rises or falls for each unit step along the x-axis.