Question

5 a ski resort is building two parallel straight ski slopes for children. one of them has a gradient of \\( \frac{1}{3} \\). the other ski slope will pass through points \\( (2, -3) \\) and \\( (s, -5) \\). find the value of \\( s \\).

Explanation:

Step1: Recall parallel lines property

Parallel lines have equal slopes.

Step2: Set up slope formula

The slope between points $(x_1,y_1)$ and $(x_2,y_2)$ is $\frac{y_2-y_1}{x_2-x_1}$. Here, slope = $\frac{1}{3}$, $(x_1,y_1)=(2,-3)$, $(x_2,y_2)=(s,-5)$.
$$\frac{-5 - (-3)}{s - 2} = \frac{1}{3}$$

Step3: Simplify numerator

Simplify the numerator of the left side.
$$\frac{-5 + 3}{s - 2} = \frac{1}{3}$$
$$\frac{-2}{s - 2} = \frac{1}{3}$$

Step4: Cross-multiply to solve for s

Cross-multiply to isolate the variable.
$$1 \times (s - 2) = -2 \times 3$$
$$s - 2 = -6$$

Step5: Solve for s

Add 2 to both sides to find s.
$$s = -6 + 2$$

Answer:

$s = -4$