To graph the equation \(3x - y = 10\), we can rearrange it into slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Starting with the original equation:
\[ 3x - y = 10 \]
We can solve for \(y\):
\[ -y = -3x + 10 \]
Multiplying through by -1 gives us:
\[ y = 3x - 10 \]
Now, we can identify that the slope \(m\) is 3, and the y-intercept \(b\) is -10. This means that the line crosses the y-axis at (0, -10).
To graph this line:
- Start at the y-intercept (0, -10) on the graph.
- Use the slope of 3 (which can be expressed as \(\frac{3}{1}\)), which means for every 3 units you move up, you move 1 unit to the right.
- From (0, -10), move up 3 units to (-10 + 3 = -7) to the point (1, -7).
- Repeat the process to find other points or use the negative slope to find points in the opposite direction.
After plotting a few points, draw a straight line through them, extending it in both directions. The resulting graph will show a straight line that slopes upwards from left to right, intersecting the y-axis at (0, -10).