Find the equation of the line whose slope is `-5/6 ` and x-intercept is 6.

Answer

To find the equation of the line with a slope of \(-\frac{5}{6}\) and an x-intercept of 6, we can follow these steps:

### Step 1: Identify the given information
- Slope (m) = \(-\frac{5}{6}\)
- X-intercept = 6, which means the point (6, 0) is on the line.

### Step 2: Use the point-slope form of the equation of a line
The point-slope form of the equation of a line is given by:
\[ y - y_1 = m(x - x_1) \]
where \((x_1, y_1)\) is a point on the line and \(m\) is the slope.

### Step 3: Substitute the known values into the equation
Using the point (6, 0) and the slope \(-\frac{5}{6}\):
\[ y - 0 = -\frac{5}{6}(x - 6) \]

### Step 4: Simplify the equation
This simplifies to:
\[ y = -\frac{5}{6}(x - 6) \]
Expanding the right-hand side:
\[ y = -\frac{5}{6}x + \frac{5}{6} \cdot 6 \]
Calculating \(\frac{5}{6} \cdot 6\):
\[ y = -\frac{5}{6}x + 5 \]

### Step 5: Rearranging to standard form
To express the equation in standard form \(Ax + By = C\):
\[ \frac{5}{6}x + y = 5 \]
Multiplying through by 6 to eliminate the fraction:
\[ 5x + 6y = 30 \]

### Final Equation
Thus, the equation of the line is:
\[ 5x + 6y = 30 \]

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