The x-intercept and the y-intercept of the line `5x – 7 = 6y`, respectively are -

Options

A. `(7)/(5)` and `(7)/(6)`
B. `(7)/(5)` and `(-7)/(6)`
C. `(7)/(5)` and `(7)/(6)`
D. `(5)/(7)` and `(6)/(7)`

Answer

To find the x-intercept and y-intercept of the line given by the equation \(5x - 7 = 6y\), we will follow these steps:

### Step 1: Find the x-intercept
To find the x-intercept, we set \(y = 0\) in the equation.

1. Start with the equation:
\[ 5x - 7 = 6y \]
2. Substitute \(y = 0\):
\[ 5x - 7 = 6(0) \]
This simplifies to:
\[ 5x - 7 = 0 \]
3. Solve for \(x\):
\[ 5x = 7 \]
\[ x = \frac{7}{5} \]

Thus, the x-intercept is \(\frac{7}{5}\).

### Step 2: Find the y-intercept
To find the y-intercept, we set \(x = 0\) in the equation.

1. Start with the original equation:
\[ 5x - 7 = 6y \]
2. Substitute \(x = 0\):
\[ 5(0) - 7 = 6y \]
This simplifies to:
\[ -7 = 6y \]
3. Solve for \(y\):
\[ y = \frac{-7}{6} \]

Thus, the y-intercept is \(-\frac{7}{6}\).

### Final Answer
The x-intercept and y-intercept of the line \(5x - 7 = 6y\) are \(\frac{7}{5}\) and \(-\frac{7}{6}\), respectively.

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