The straight line L₁ has equation y = 3x - 4 - Edexcel - GCSE Maths - Question 16 - 2020 - Paper 1
Question 16
The straight line L₁ has equation y = 3x - 4.
The straight line L₂ is perpendicular to L₁, and passes through the point (9, 5).
Find an equation of line L₂.
Worked Solution & Example Answer:The straight line L₁ has equation y = 3x - 4 - Edexcel - GCSE Maths - Question 16 - 2020 - Paper 1
Step 1
Find the gradient of L₁
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Answer
The equation of line L₁ is given as (y = 3x - 4). The gradient (slope) of this line is the coefficient of x, which is 3.
Step 2
Determine the gradient of L₂
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Answer
Since L₂ is perpendicular to L₁, its gradient (m₂) can be found using the negative reciprocal of L₁'s gradient. Therefore, (m₂ = -\frac{1}{3}).
Step 3
Use the point (9, 5) to find the equation of L₂
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Answer
The point-slope form of a linear equation is given by (y - y_1 = m(x - x_1)). Here, (m = -\frac{1}{3}), (x_1 = 9), and (y_1 = 5). Substituting these values, we get:
[y - 5 = -\frac{1}{3}(x - 9)]
Expanding this gives:
[y - 5 = -\frac{1}{3}x + 3]
Simplifying,
[y = -\frac{1}{3}x + 8]
Thus, the equation of line L₂ is (y = -\frac{1}{3}x + 8).
