To find the x- and y-intercepts of the line given by the equation \(7x + 2y = 14\), we can follow these steps:
Finding the x-intercept:
The x-intercept occurs when \(y = 0\). To find the x-intercept, we substitute \(y = 0\) into the equation:
\[ 7x + 2(0) = 14 \]
This simplifies to:
\[ 7x = 14 \]
Now, solve for \(x\):
\[ x = \frac{14}{7} = 2 \]
Thus, the x-intercept is \((2, 0)\).
Finding the y-intercept:
The y-intercept occurs when \(x = 0\). To find the y-intercept, we substitute \(x = 0\) into the equation:
\[ 7(0) + 2y = 14 \]
This simplifies to:
\[ 2y = 14 \]
Now, solve for \(y\):
\[ y = \frac{14}{2} = 7 \]
Thus, the y-intercept is \((0, 7)\).
Summary of Intercepts:
- x-intercept: \((2, 0)\)
- y-intercept: \((0, 7)\)