The equation of the line is given by

To gain a clearer understanding of how we derive this equation, let’s break it down step by step. The standard form of a straight line is

where $m$ denotes the slope (or gradient) of the line and $c$ indicates the y-intercept. The y-intercept is the point at which the line intersects the y-axis.

In our case, we have a slope of $-3$ and a y-intercept of $6$. The slope provides insight into the steepness of the line and its direction. Specifically, a slope of $-3$ indicates that for every 1 unit you move to the right along the x-axis, the line descends by 3 units. The y-intercept of $6$ tells us that the line crosses the y-axis at the coordinate point $(0, 6)$.

By substituting the provided values into the general equation $y = mx + c$, we replace $m$ with $-3$ and $c$ with $6$. This results in the specific equation for this line:

This equation encapsulates all the essential information about the line. For any given value of $x$, you can determine the corresponding $y$ value by substituting $x$ into the equation. For instance, if $x = 2$, we can calculate $y$ as follows:

Thus, the point $(2, 0)$ lies on the line. This method of expressing a straight line mathematically is both straightforward and powerful.