he line y=1/4x+2 meets the y axis at the point B. The point C has coordinates (-5,3). Find the gradient of the line joining the points B and C

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.

The line y = 1/4x + 2 meets the y-axis at the point B. The point C has coordinates (-5, 3). Find the gradient of the line joining the points B and C.

Learn how to find the gradient of a line joining two points B(0, 2) and C(-5, 3) using the gradient formula. This problem covers key geometry concepts and is suitable for students in Grades 8-10.

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