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A straight line with gradient 4 passes through the point (1, 5) - OCR - GCSE Maths - Question 23 - 2019 - Paper 1

Question 23

A straight line with gradient 4 passes through the point (1, 5). Find the equation of the line in the form y = mx + c.

Worked Solution & Example Answer:A straight line with gradient 4 passes through the point (1, 5) - OCR - GCSE Maths - Question 23 - 2019 - Paper 1

Step 1

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Answer

The gradient (m) of the line is given as 4. The line passes through the point (1, 5). This means the coordinates of the point are x = 1 and y = 5.

Step 2

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Answer

The point-slope form of the equation of a straight line is given by:

$y - y_1 = m(x - x_1)$

Substituting the known values into the equation, we have:

$y - 5 = 4(x - 1)$

Step 3

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Answer

To convert this to the slope-intercept form y = mx + c, we simplify:

$y - 5 = 4x - 4$

Adding 5 to both sides gives:

$y = 4x + 1$

Thus, the equation of the line in the required form is:

$y = 4x + 1$

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