The equation of a line is given as $2y = 7x - 5$. We need to find the gradient and the y-intercept of the line.

1. Problem Description

The equation of a line is given as $2y = 7x - 5$. We need to find the gradient and the y-intercept of the line.

2. Solution Steps

To find the gradient and y-intercept of the line, 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.

First, divide the given equation by 2:

$2y = 7x - 5$

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

Now, the equation is in the form $y = mx + c$.

The gradient, $m$, is the coefficient of $x$, which is $\frac{7}{2}$.

The y-intercept, $c$, is the constant term, which is $-\frac{5}{2}$.

3. Final Answer

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

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