The problem gives the equation of a line as $2y = 7x - 5$. It asks for the gradient and y-intercept of the line.

1. Problem Description

The problem gives the equation of a line as $2y = 7x - 5$. It asks for the gradient and y-intercept of the line.

2. Solution Steps

First, we need to rewrite the equation in the slope-intercept form, which is $y = mx + c$, where $m$ is the gradient and $c$ is the y-intercept.

We are given the equation $2y = 7x - 5$.

To isolate $y$, we divide both sides of the equation by 2:

$y = \frac{7x - 5}{2}$

$y = \frac{7}{2}x - \frac{5}{2}$

Comparing this with $y = mx + c$, we find:

Gradient, $m = \frac{7}{2}$

y-intercept, $c = -\frac{5}{2}$

3. Final Answer

a) The gradient of the line is $\frac{7}{2}$.

b) The y-intercept of the line is $-\frac{5}{2}$.