The problem asks us to find the gradient (slope) and the y-intercept of two linear equations: a) $y = -2x + 8$ b) $y = x + \frac{9}{8}$

1. Problem Description

The problem asks us to find the gradient (slope) and the y-intercept of two linear equations:

a) $y = -2x + 8$

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

2. Solution Steps

The general form of a linear equation is $y = mx + c$, where $m$ is the gradient (slope) and $c$ is the y-intercept.

a) The equation is given by $y = -2x + 8$.

Comparing this with the general form $y = mx + c$, we can identify the gradient and y-intercept.

Gradient, $m = -2$

Y-intercept, $c = 8$

b) The equation is given by $y = x + \frac{9}{8}$.

Comparing this with the general form $y = mx + c$, we can identify the gradient and y-intercept.

We can rewrite the equation as $y = 1x + \frac{9}{8}$.

Gradient, $m = 1$

Y-intercept, $c = \frac{9}{8}$

3. Final Answer

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

b) Gradient: 1, y-intercept: 9/8