The problem asks us to find the gradient ($m$) and the y-intercept for each of the two given graphs (a and b).

1. Problem Description

The problem asks us to find the gradient ($m$) and the y-intercept for each of the two given graphs (a and b).

2. Solution Steps

Graph a:

We are given one point on the line, (3, 5). From the graph, we can see that the line passes through the origin (0, 0).

We can use these two points to find the gradient $m$. The formula for gradient is:

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

Using the points (0, 0) and (3, 5), we have:

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

The y-intercept is the point where the line crosses the y-axis. From the graph, we can see that the line crosses the y-axis at (0, 0). Therefore, the y-intercept is

0.

Graph b:

We are given two points on the line, (0, 4) and (1, 0).

We can use these two points to find the gradient $m$. The formula for gradient is:

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

Using the points (0, 4) and (1, 0), we have:

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

The y-intercept is the point where the line crosses the y-axis. From the graph, we can see that the line crosses the y-axis at (0, 4). Therefore, the y-intercept is

4.

3. Final Answer

For graph a:

Gradient, $m = \frac{5}{3}$

y-intercept = 0

For graph b:

Gradient, $m = -4$

y-intercept = 4