The problem asks us to find the gradient and y-intercept for each of the given linear equations. The equations are in the form $y = mx + c$, where $m$ is the gradient and $c$ is the y-intercept.

1. Problem Description

The problem asks us to find the gradient and y-intercept for each of the given linear equations. The equations are in the form $y = mx + c$, where $m$ is the gradient and $c$ is the y-intercept.

2. Solution Steps

a) The equation is $y = 5x - 2$. Comparing this to $y = mx + c$, we can see that the gradient $m = 5$ and the y-intercept $c = -2$.

b) The equation is $y = -4x$. This can be written as $y = -4x + 0$. Comparing this to $y = mx + c$, we have $m = -4$ and $c = 0$.

c) The equation is $y = \frac{1}{2}x + 7$. Comparing this to $y = mx + c$, we have $m = \frac{1}{2}$ and $c = 7$.

3. Final Answer

a) Gradient: 5, y-intercept: -2

b) Gradient: -4, y-intercept: 0

c) Gradient: $\frac{1}{2}$, y-intercept: 7