The problem asks to calculate the gradient of the line joining two given points in two separate cases. a) $(3, 0)$ and $(7, 1)$ b) $(-9, 6)$ and $(0, 3)$

1. Problem Description

The problem asks to calculate the gradient of the line joining two given points in two separate cases.

a) $(3, 0)$ and $(7, 1)$

b) $(-9, 6)$ and $(0, 3)$

2. Solution Steps

The gradient ($m$) of a line joining two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:

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

a) Given points are $(3, 0)$ and $(7, 1)$.

Let $(x_1, y_1) = (3, 0)$ and $(x_2, y_2) = (7, 1)$.

Using the gradient formula:

$m = \frac{1 - 0}{7 - 3} = \frac{1}{4}$

b) Given points are $(-9, 6)$ and $(0, 3)$.

Let $(x_1, y_1) = (-9, 6)$ and $(x_2, y_2) = (0, 3)$.

Using the gradient formula:

$m = \frac{3 - 6}{0 - (-9)} = \frac{-3}{9} = -\frac{1}{3}$

3. Final Answer

a) The gradient of the line joining $(3, 0)$ and $(7, 1)$ is $\frac{1}{4}$.

b) The gradient of the line joining $(-9, 6)$ and $(0, 3)$ is $-\frac{1}{3}$.