Obtain the equation of a straight line passing through (3, 15) whose slope = 3$\frac{1}{5}$.

Analysis

To find the equation of a straight line when you are given a point $(x_1, y_1)$ and the slope ($m$), you use the Point-Slope Form of a linear equation.

Concept

The point-slope formula is:

Where:

• $(x_1, y_1) = (3, 15)$
• $m = 3\frac{1}{5} = \frac{16}{5}$

Solution

Step 1: Substitute the values into the formula.

Step 2: Eliminate the fraction by multiplying both sides by 5.

Step 3: Expand both sides.

Step 4: Rearrange the equation to match the format of the options (moving all terms to one side). Subtract $16x$ and add $48$ to both sides to set the equation to zero:

Comparing this result to the given options, it matches option C.

Tip

When dealing with fractional slopes in exam questions, always convert the mixed fraction to an improper fraction immediately. Multiplying the entire equation by the denominator is the fastest way to clear the fraction and avoid calculation errors with decimals!