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A is the point with coordinates (5, 9) B is the point with coordinates (d, 15) The gradient of the line AB is 3 Work out the value of d. - Edexcel - GCSE Maths - Question 7 - 2018 - Paper 2

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A is the point with coordinates (5, 9) B is the point with coordinates (d, 15) The gradient of the line AB is 3 Work out the value of d.

Worked Solution & Example Answer:A is the point with coordinates (5, 9) B is the point with coordinates (d, 15) The gradient of the line AB is 3 Work out the value of d. - Edexcel - GCSE Maths - Question 7 - 2018 - Paper 2

Step 1

Use the gradient formula

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Answer

The gradient (m) of a line through points A(x1, y1) and B(x2, y2) is given by the formula:

m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}

Here, we know that:

  • A(5, 9) corresponds to (x1, y1)
  • B(d, 15) corresponds to (x2, y2) Thus, we can substitute the coordinates into the formula:

3=15−9d−53 = \frac{15 - 9}{d - 5}

Step 2

Rearranging the equation

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Answer

Now, we can rearrange the equation to isolate d:

  1. Start with: 3=6d−53 = \frac{6}{d - 5}
  2. Multiply both sides by (d - 5): 3(d−5)=63(d - 5) = 6
  3. Expand the equation: 3d−15=63d - 15 = 6
  4. Add 15 to both sides: 3d=213d = 21

Step 3

Solve for d

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Answer

Finally, divide both sides by 3:

d=213=7d = \frac{21}{3} = 7

Thus, the value of d is 7.

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