Question 22 of 70intermediate🔧 ApplyShort Answer3 marks

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2,3)(2, 3).

Correct Answer

Since the line cuts off equal intercepts on the coordinate axes, let the intercepts be a on both axes. Using the intercept form of the equation of a line: x/a + y/a = 1. This simplifies to x + y = a. Since the line passes through the point (2, 3), substituting these coordinates gives 2 + 3 = a, so a = 5. Therefore, the equation of the line is x + y = 5 or x + y - 5 = 0.

Exercise: EXERCISE 9.2 | Q: 11 | (Page 14)
For More Understanding

Explanation

The textbook provides the intercept form of a line as x/a + y/b = 1 (Section 9.3.5), where a and b are the x-intercept and y-intercept respectively. Since the line cuts equal intercepts on both axes, we have a = b. Substituting the point (2, 3) into the simplified equation allows us to determine the value of the intercept.

Solution Steps

  1. Step 1: Let the equal intercepts be 'a' on both axes. Using intercept form: x/a + y/a = 1

  2. Step 2: Simplify to get x + y = a

  3. Step 3: Since the line passes through (2, 3), substitute: 2 + 3 = a, giving a = 5

  4. Step 4: The required equation is x + y = 5 or x + y - 5 = 0

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