The problem asks to find the gradient and the y-intercept of three lines given in the form $y = mx + c$, where $m$ is the gradient and $c$ is the y-intercept. a) $y = -2x + 8$ b) $y = x + \frac{9}{8}$ c) $y = -\frac{10x}{9} - 10$

1. Problem Description

The problem asks to find the gradient and the y-intercept of three lines given in the form $y = mx + c$, where $m$ is the gradient and $c$ is the y-intercept.

a) $y = -2x + 8$

b) $y = x + \frac{9}{8}$

c) $y = -\frac{10x}{9} - 10$

2. Solution Steps

We will identify the gradient ($m$) and y-intercept ($c$) for each equation by comparing it to the standard form $y = mx + c$.

a) $y = -2x + 8$

Comparing with $y = mx + c$, we can see that the gradient $m = -2$ and the y-intercept $c = 8$.

b) $y = x + \frac{9}{8}$

Comparing with $y = mx + c$, we can see that the gradient $m = 1$ and the y-intercept $c = \frac{9}{8}$.

c) $y = -\frac{10x}{9} - 10$

Rewriting as $y = -\frac{10}{9}x - 10$.

Comparing with $y = mx + c$, we can see that the gradient $m = -\frac{10}{9}$ and the y-intercept $c = -10$.

3. Final Answer

a) Gradient: $-2$, y-intercept: $8$

b) Gradient: $1$, y-intercept: $\frac{9}{8}$

c) Gradient: $-\frac{10}{9}$, y-intercept: $-10$