Quick questions on Gradient and intercept for HSC Maths Standard 2

The gradient of a line, usually called $m$, is the vertical rise divided by the horizontal run between any two points on it:

The sign of the gradient tells you which way the line tilts, before you even look at how steep it is. Read every line left to right (the direction of increasing $x$) and ask what $y$ is doing.

The $y$-intercept is the value of $y$ where the line crosses the vertical axis, the point $(0, b)$. You read it straight off a graph by finding where the line cuts the $y$-axis: no calculation needed. The letter $b$ is the usual name for it. In a real context the $y$-intercept is the starting value of the relationship, what $y$ equals when $x$ is zero: a fixed monthly fee before you use any data, a taxi flagfall before the car moves, a tank's level before you start draining it.

When you are given two points rather than a graph, you do not need to plot anything: the gradient formula computes the rise over run straight from the coordinates. For points $(x_1, y_1)$ and $(x_2, y_2)$,