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WAEC Further Mathematics 2014 Paper

Question : 3

Total: 40

Given that

3x + 4y + 6 = 0

4x - by + 3 = 0

are perpendicular, find the value of b.

Solution:

Concept:

For two perpendicular lines, the product of their slopes is

-1

Explanation:

Write the first equation in slope-intercept form.

3x + 4y + 6 = 0

4y = -3x - 6

y = -\frac{3}{4}x - \frac{3}{2}

So, slope

m_1 = -\frac{3}{4}

Write the second equation in slope-intercept form.

4x - by + 3 = 0

by = 4x + 3

y = \frac{4}{b}x + \frac{3}{b}

So, slope

m_2 = \frac{4}{b}

Since the lines are perpendicular:

m_1 \times m_2 = -1

-\frac{3}{4} \times \frac{4}{b} = -1

-\frac{3}{b} = -1

b = 3

Answer:

b = 3

, which is option B.

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