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The graph shows two parallel lines, Line A and Line B - OCR - GCSE Maths - Question 24 - 2019 - Paper 1

Question 24

The graph shows two parallel lines, Line A and Line B. Line A has equation $y = 6x + 7$. Line B passes through the point (4, 26). Find the equation of Line B.

Worked Solution & Example Answer:The graph shows two parallel lines, Line A and Line B - OCR - GCSE Maths - Question 24 - 2019 - Paper 1

Step 1

Find the slope of Line A

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Answer

The slope of Line A can be obtained from its equation, which is in the slope-intercept form, $y = mx + b$ where $m$ is the slope. For Line A, the slope $m = 6$ .

Step 2

Use the point-slope form to find Line B's equation

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Answer

Since Line B is parallel to Line A, it has the same slope. Using the point-slope form of the line equation, $y - y_1 = m(x - x_1)$ , where $(x_1, y_1) = (4, 26)$ and $m = 6$ , we get:

$y - 26 = 6(x - 4)$ .

Simplifying this gives:

$y - 26 = 6x - 24$

Therefore,

$y = 6x + 2$ .

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