Question 18 of 70beginner🔧 ApplyVery Short1 mark

In Exercises 1 to 8, find the equation of the line which satisfy the given conditions: Passing through the points (−1,1)(-1, 1) and (2,−4)(2, -4).

Correct Answer

5x + 3y + 2 = 0

Exercise: EXERCISE 9.2 | Q: 7 | (Page 14)
For More Understanding

Explanation

This question asks for the equation of a line passing through two given points. According to the Two-point form provided in section 9.3.3 of the textbook, the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is given by: y - y₁ = (y₂ - y₁)/(x₂ - x₁) × (x - x₁). Here, the given points are (-1, 1) and (2, -4). Substituting these values and simplifying gives the required equation.

Solution Steps

  1. Step 1: Identify the given points: (x₁, y₁) = (-1, 1) and (x₂, y₂) = (2, -4).

  2. Step 2: Using the two-point form: y - y₁ = (y₂ - y₁)/(x₂ - x₁) × (x - x₁)

  3. Step 3: Substitute the values: y - 1 = (-4 - 1)/(2 - (-1)) × (x - (-1))

  4. Step 4: Simplify the slope: y - 1 = -5/3 × (x + 1)

  5. Step 5: Multiply by 3 and rearrange: 3(y - 1) = -5(x + 1), which gives 3y - 3 = -5x - 5

  6. Step 6: Final equation: 5x + 3y + 2 = 0

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