Question 36 of 70intermediate🔧 ApplyShort Answer3 marks

Find equation of the line parallel to the line 3x−4y+2=03x - 4y + 2 = 0 and passing through the point (−2,3)(-2, 3).

Correct Answer

3x - 4y + 18 = 0

Exercise: EXERCISE 9.3 | Q: 6 | (Page 17)
For More Understanding

Explanation

This question tests understanding of parallel lines and the point-slope form. From the textbook context, parallel lines have the same slope. The point-slope form (Equation 1 in section 9.3.2) states: y - y₀ = m(x - x₀). First, we find the slope of the given line by converting it to slope-intercept form. Then we use this slope with the given point to find the required equation.

Solution Steps

  1. Step 1: Find the slope of the given line 3x - 4y + 2 = 0. Rewriting: 4y = 3x + 2, so y = (3/4)x + 1/2. Therefore, slope m = 3/4.

  2. Step 2: Since parallel lines have the same slope, the required line also has slope m = 3/4.

  3. Step 3: Using the point-slope form y - y₀ = m(x - x₀) with point (-2, 3) and slope 3/4: y - 3 = (3/4)(x + 2).

  4. Step 4: Simplifying: 4(y - 3) = 3(x + 2), which gives 4y - 12 = 3x + 6.

  5. Step 5: Rearranging to standard form: 3x - 4y + 18 = 0 is the required equation.

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