Find the equation of the line with x-intercept 5 and a point on it (-3, 2).

Answer

To find the equation of the line with an x-intercept of 5 and a point on it (-3, 2), we can follow these steps:

### Step 1: Identify the Points
The x-intercept of the line is the point where the line crosses the x-axis. This means at the x-intercept, the y-coordinate is 0. Therefore, the x-intercept point is:
- Point A (5, 0)

We also have another point on the line:
- Point B (-3, 2)

### Step 2: Calculate the Slope of the Line
The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is calculated using the formula:
\[ m = \frac{y2 - y1}{x2 - x1} \]

Substituting the coordinates of points A and B:
- A (5, 0) → (x1, y1) = (5, 0)
- B (-3, 2) → (x2, y2) = (-3, 2)

Now, substituting into the slope formula:
\[ m = \frac{2 - 0}{-3 - 5} = \frac{2}{-8} = -\frac{1}{4} \]

### Step 3: Use the Point-Slope Form of the Equation
The point-slope form of the equation of a line is given by:
\[ y - y1 = m(x - x1) \]

Using point A (5, 0) and the slope we calculated:
- y1 = 0
- m = -\frac{1}{4}
- x1 = 5

Substituting these values into the point-slope form:
\[ y - 0 = -\frac{1}{4}(x - 5) \]

### Step 4: Simplify the Equation
Now, simplify the equation:
\[ y = -\frac{1}{4}(x - 5) \]
\[ y = -\frac{1}{4}x + \frac{5}{4} \]

### Step 5: Rearrange to Standard Form
To express the equation in standard form \( Ax + By = C \), we can rearrange:
\[ \frac{1}{4}x + y = \frac{5}{4} \]

Multiplying through by 4 to eliminate the fraction:
\[ x + 4y = 5 \]

### Final Answer
Thus, the equation of the line is:
\[ x + 4y = 5 \]