Answer:
Step-by-step explanation:
To find the equation of the line passing through the points \((3,0)\) and \((6,3)\), we can follow these steps:
1. **Calculate the slope (\(m\)) of the line** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute \((x_1, y_1) = (3, 0)\) and \((x_2, y_2) = (6, 3)\):
\[
m = \frac{3 - 0}{6 - 3} = \frac{3}{3} = 1
\]
2. **Use the point-slope form of the equation of a line**, which is:
\[
y - y_1 = m(x - x_1)
\]
Choose either point to substitute into the equation. Let's use \((3, 0)\) and \(m = 1\):
\[
y - 0 = 1(x - 3)
\]
Simplify the equation:
\[
y = x - 3
\]
3. **Verify the solution** by substituting the other point \((6, 3)\) into the equation to ensure it satisfies the line:
\[
y = 6 - 3 = 3
\]
Since \(y = 3\) when \(x = 6\), the point \((6, 3)\) lies on the line.
Therefore, the equation of the line passing through the points \((3,0)\) and \((6,3)\) is \( \boxed{y = x - 3} \).
