A straight line passing through the points (1, 3) and (5, k) has a gradient of 2. What is … — JAMB UTME

A straight line passing through the points $(1, 3)$ and $(5, k)$ has a gradient of $2$ . What is the value of $k$ ?

Answer: 11

The value of

k

11

The gradient

m

of a line passing through

(x_1, y_1)

and

(x_2, y_2)

is given by

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

. Substituting

(1, 3)

(5, k)

, and

m = 2

yields

2 = \frac{k - 3}{5 - 1} = \frac{k - 3}{4}

. Multiplying by

4

gives

8 = k - 3

, so

k = 11

Recall the slope/gradient formula for a straight line.

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

The gradient of a straight line passing through two points is the ratio of vertical change to horizontal change.

Substitute the known point coordinates and gradient into the formula.

2 = \frac{k - 3}{5 - 1}

We are given

(x_1, y_1) = (1, 3)

(x_2, y_2) = (5, k)

, and gradient

m = 2

Simplify and solve for

k

2 = \frac{k - 3}{4} \implies 8 = k - 3 \implies k = 11

Multiplying both sides by

4

clears the fraction, and adding

3

isolates

k

Gradient of a straight line passing through two points

Estimated Time:45s

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