The equation given is:

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

This equation represents a linear function in the form $y = mx + b$, where:

• $m = \frac{1}{2}$ is the slope, indicating that for every increase of 1 in $x$, $y$ increases by $\frac{1}{2}$.
• $b = -6$ is the y-intercept, meaning the line crosses the y-axis at $y = -6$.

Key Properties

1. Slope (m): $\frac{1}{2}$, so the line rises by 1 unit for every 2 units it moves to the right.
2. Y-intercept (b): -6, so the line passes through the point (0, -6).
3. X-intercept: To find where the line crosses the x-axis, set $y = 0$ and solve for $x$: $0 = \frac{1}{2}x - 6 \implies x = 12$ So, the x-intercept is at (12, 0).

Graphing Steps

1. Plot the y-intercept at (0, -6).
2. Use the slope to find another point. From (0, -6), go up 1 unit and right 2 units to find (2, -5).
3. Draw a line through these points, extending it in both directions.

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Related Questions

1. What does it mean if the slope is negative?
2. How would this equation change if the y-intercept were zero?
3. How would the graph look if the slope were steeper, like 2?
4. What is the relationship between slope and angle of the line?
5. How can you determine the slope and intercept if only the graph is given?

Tip

For any linear equation, the slope tells you the "steepness" and direction of the line!