Question

Find the x- and y-intercepts for the line given by the equation 7x + 2y =14

Answer 1

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**: \((0, 7)\)