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JAMB Mathematics 2014 Paper

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Question : 26

Total: 47

The gradient of a line joining (x,4) and (1,2) is

\frac{1}{2}

. Find the value of x

5
3
-3
-5

Solution:

Concept:

Use the gradient formula for a line through two points and solve for the unknown coordinate.

Explanation:

The gradient

m

of a line joining

(x_1, y_1)

and

(x_2, y_2)

is given by:

m = \frac{y_2 - y_1}{x_2 - x_1}

Here,

(x_1, y_1) = (x, 4)

and

(x_2, y_2) = (1, 2)

.

Substitute the known gradient

m = \frac{1}{2}

:

\frac{1}{2} = \frac{2 - 4}{1 - x}

Simplify the numerator:

\frac{1}{2} = \frac{-2}{1 - x}

Cross-multiply:

1 - x = 2(-2)

1 - x = -4

Solve for

x

:

-x = -4 - 1

-x = -5

x = 5

Answer:

x = 5

(Option A).

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