The problem asks to determine the gradient, y-intercept, and the equation of the graph for each of the two given graphs.

1. Problem Description

The problem asks to determine the gradient, y-intercept, and the equation of the graph for each of the two given graphs.

2. Solution Steps

Graph 1:

a) The gradient (slope) $m$ is given by the formula $m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$.

From the graph, we can identify two points on the line. For example, $(0, 4)$ and $(1, 0)$.

Then, $m = \frac{0-4}{1-0} = \frac{-4}{1} = -4$.

b) The y-intercept is the value of $y$ when $x=0$. From the graph, the y-intercept is

4.

c) The equation of a line is given by $y = mx + c$, where $m$ is the gradient and $c$ is the y-intercept.

Substituting $m = -4$ and $c = 4$ gives $y = -4x + 4$.

Graph 2:

a) From the graph, we can identify two points on the line. For example, $(0, -10)$ and $(1, -8)$.

Then, $m = \frac{-8 - (-10)}{1 - 0} = \frac{-8 + 10}{1} = \frac{2}{1} = 2$.

b) The y-intercept is the value of $y$ when $x=0$. From the graph, the y-intercept is -

1

0.

c) The equation of a line is given by $y = mx + c$, where $m$ is the gradient and $c$ is the y-intercept.

Substituting $m = 2$ and $c = -10$ gives $y = 2x - 10$.

3. Final Answer

Graph 1:

a) Gradient: -4

b) y-intercept: 4

c) Equation: $y = -4x + 4$

Graph 2:

a) Gradient: 2

b) y-intercept: -10

c) Equation: $y = 2x - 10$