The equation of the line is given as $y = \frac{1}{4}x + 2$. To find the point where this line meets the y-axis, we set $x = 0$, since any point on the y-axis has $x = 0$.

So, when $x = 0$:

$y = \frac{1}{4}(0) + 2 = 2$

Thus, the coordinates of point $B$ are $(0, 2)$.

Now, we are asked to find the gradient (slope) of the line joining the points $B(0, 2)$ and $C(-5, 3)$.

The formula for the gradient of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Substituting $(x_1, y_1) = (0, 2)$ and $(x_2, y_2) = (-5, 3)$:

$m = \frac{3 - 2}{-5 - 0} = \frac{1}{-5} = -\frac{1}{5}$

Thus, the gradient of the line joining points $B$ and $C$ is $-\frac{1}{5}$.

Would you like more details, or do you have any questions?

Here are 5 related questions:

1. How do you find the gradient of a vertical line?
2. What is the significance of the gradient being negative?
3. How do you calculate the equation of a line passing through two given points?
4. What is the slope-intercept form of a line?
5. Can two non-parallel lines have the same gradient?

Tip: The gradient tells you the steepness of the line and whether it rises or falls as you move from left to right.