To find the x-intercept of the line given by the equation \(y = \frac{2}{7}x - 2\), we set \(y\) to 0 and solve for \(x\).
-
Set \(y = 0\): \[ 0 = \frac{2}{7}x - 2 \]
-
Add 2 to both sides: \[ 2 = \frac{2}{7}x \]
-
Multiply both sides by \(\frac{7}{2}\) to solve for \(x\): \[ x = 2 \cdot \frac{7}{2} = 7 \]
Thus, the x-intercept of the line is \(x = 7\). Therefore, the x-intercept is at the point \((7, 0)\).