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A straight line passes through the point (8, 1) and is perpendicular to the line $y = 4x - 2$ - OCR - GCSE Maths - Question 13 - 2021 - Paper 1

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A straight line passes through the point (8, 1) and is perpendicular to the line $y = 4x - 2$. Find the equation of the line, giving your answer in the form $y = mx... show full transcript

Worked Solution & Example Answer:A straight line passes through the point (8, 1) and is perpendicular to the line $y = 4x - 2$ - OCR - GCSE Maths - Question 13 - 2021 - Paper 1

Step 1

Find the slope of the given line

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Answer

The given line is y=4x−2y = 4x - 2, which can be compared to the slope-intercept form y=mx+cy = mx + c. Here, the slope mm is 4. Thus, the slope of the line perpendicular to it will be the negative reciprocal of 4:

mperpendicular=−14m_{perpendicular} = -\frac{1}{4}

Step 2

Use point-slope form to find the equation

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Answer

We use the point-slope form of the equation of a line, which is given by:

y−y1=m(x−x1)y - y_1 = m(x - x_1)

Substituting the point (8,1)(8, 1) and the slope −14-\frac{1}{4}, we have:

y−1=−14(x−8)y - 1 = -\frac{1}{4}(x - 8)

Step 3

Simplify to the slope-intercept form

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Answer

Now we simplify this to find the equation in the form y=mx+cy = mx + c:

y−1=−14x+2y - 1 = -\frac{1}{4}x + 2 y=−14x+3y = -\frac{1}{4}x + 3

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