To graph the equation $x - 2y = 6$ using intercepts, we’ll find the points where the line intersects the x-axis and y-axis.

Step 1: Rewrite in Standard Form

The equation is already in standard form: $x - 2y = 6$

Step 2: Find the x-intercept

To find the x-intercept, set $y = 0$ in the equation: $x - 2(0) = 6 \Rightarrow x = 6$ So, the x-intercept is $(6, 0)$.

Step 3: Find the y-intercept

To find the y-intercept, set $x = 0$ in the equation: $0 - 2y = 6 \Rightarrow y = -3$ So, the y-intercept is $(0, -3)$.

Step 4: Plot the Points and Draw the Line

1. Plot the point $(6, 0)$ on the x-axis.
2. Plot the point $(0, -3)$ on the y-axis.
3. Draw a straight line through these points to complete the graph.

Would you like further details or have any questions?

Related Questions

1. How would you find the slope of the line from this equation?
2. What would be the slope-intercept form of the equation $x - 2y = 6$?
3. If you changed the equation to $x - 2y = 4$, how would the intercepts change?
4. How do you determine if two lines are parallel based on their equations?
5. What is the relationship between the standard form and slope-intercept form of a line?

Tip

When graphing a line, using intercepts is quick and efficient, especially for lines in standard form like $Ax + By = C$.