Let's go through the questions one by one based on the image you uploaded. I'll provide the solutions in detail.

Questions 1-5 (Based on the first graph):

1. What are the coordinates of point B?

   • Answer: To find the coordinates of point B, locate it on the graph. It appears to be at (4, -2).

2. What point is on the x-axis?

   • Answer: A point on the x-axis will have a y-coordinate of 0. From the graph, point D seems to be on the x-axis at (2, 0).

3. At what quadrant or axis is point C located?

   • Answer: Point C is in the third quadrant since both its x and y coordinates are negative. Its approximate location is (-3, -4).

4. What is the gradient of line AE?

   • Answer: To find the gradient (slope) of line AE, use the formula: $\text{Gradient} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}$ For points A (6, 3) and E (0, -1): $\text{Gradient} = \frac{3 - (-1)}{6 - 0} = \frac{4}{6} = \frac{2}{3}$ So, the gradient is $\frac{2}{3}$.

5. What is the gradient of the line parallel to the x-axis?

   • Answer: A line parallel to the x-axis has a gradient (slope) of 0, because there is no change in the y-value as x changes.

Questions 6-11 (Based on the second graph and equation):

6. What is the value of $y$ when $x = 3$?

   • Answer: Using the equation $y = 3x - 5$: $y = 3(3) - 5 = 9 - 5 = 4$ So, $y = 4$ when $x = 3$.

7. What is the gradient of the line?

   • Answer: The given equation is $y = 3x - 5$. The coefficient of $x$ (which is 3) is the gradient of the line. Thus, the gradient is 3.

8. At what value of $y$ does the line intersect the y-axis?

   • Answer: The y-intercept occurs when $x = 0$. Substituting into the equation: $y = 3(0) - 5 = -5$ So, the line intersects the y-axis at $y = -5$.

9. At what value of $x$ does the line intersect the x-axis?

   • Answer: The x-intercept occurs when $y = 0$. Set $y = 0$ in the equation: $0 = 3x - 5 \implies 3x = 5 \implies x = \frac{5}{3}$ So, the line intersects the x-axis at $x = \frac{5}{3}$.

10. Which of the axes will the graph of the line $y = -3$ be parallel to?

    • Answer: The line $y = -3$ is a horizontal line, meaning it is parallel to the x-axis.

11. What is the equation of the line whose gradient is $\frac{1}{2}$ and y-intercept is at $-3$?

    • Answer: The equation of a line is given by: $y = mx + c$ where $m$ is the gradient and $c$ is the y-intercept. Substituting $m = \frac{1}{2}$ and $c = -3$: $y = \frac{1}{2}x - 3$ So, the equation of the line is $y = \frac{1}{2}x - 3$.

Let me know if you'd like more details or clarifications on any of these questions.

Here are 5 follow-up questions based on the above:

1. What is the significance of the gradient of a line in geometry?
2. How can you determine if two lines are parallel by comparing their gradients?
3. What is the general equation of a line, and what do its components represent?
4. How do you calculate the x-intercept and y-intercept of a linear equation?
5. What is the relationship between horizontal lines and their gradients?

Tip: To quickly find intercepts from a linear equation in standard form, substitute $x = 0$ for the y-intercept and $y = 0$ for the x-intercept.