Find the equation of a line that passes through the point $(2, 5)$ and is parallel to the line $3 x - 4 y + 12 = 0$ .

medium 2 marks Class 9 · Mathematics · Lines and Angles

Answer

3x-4y+14=0

The correct answer is 3x-4y+14=0 — Step 6: Thus the required equation is $3 x - 4 y + 14 = 0$ .

Step-by-step solution

Step 1: Rewrite the given line in slope–intercept form: $3 x - 4 y + 12 = 0; \Rightarrow; y = \frac{3}{4} x + 3$ , so its slope is $m = \frac{3}{4}$ .
Step 2: A line parallel to this one has the same slope $m = \frac{3}{4}$ .
Step 3: Use the point–slope form with point $(2, 5)$ : $y - 5 = \frac{3}{4} (x - 2)$ .
Step 4: Multiply by $4$ to eliminate fractions: $4 y - 20 = 3 x - 6$ .
Step 5: Rearrange to standard form: $3 x - 4 y + 14 = 0$ .
Step 6: Thus the required equation is $3 x - 4 y + 14 = 0$ .

Common mistake: Using the wrong sign for the constant term

Concept tested: Parallel lines and linear equations