Graphical Representation of a Function that Represents Direct Proportionality

When $a > 0$ is positive: the line is ascending

When $a < 0$ is negative: the line is descending

When $a = 0$: the line is parallel to the $X$ axis

$b$ the y-intercept $Y$

$b$ indicates at which point the line crosses the $Y$ axis.

If $b$ has a positive coefficient, the line will intersect the positive part of the $Y$ axis at the point $b$.

If b has a negative coefficient, the line will intersect the negative part of the $Y$ axis at the point $b$.

If $b=0$, the line will cross the $Y$ axis at the origin where $Y=0$.

To know exactly what the graph of the line's equation looks like, we will have to examine both parameters at the same time, both a and $b$.

$y=5x-4$
We will examine the linear equation.

$a=5$ The slope is positive, the line ascends
$b=-4$ The line crosses the $Y$ axis at the point where $Y=-4$

We will plot the graph based on the data:

Keep in mind that this is just a sketch.

If you want to draw the graph accurately, you can construct a table of values for $X$ and $Y$ and find out the points that form the line.

The function $y=2X$ represents a direct proportionality between the values of $X$ and $Y$. That is, for each value of $X$ that we input, the value of $Y$ will be double.

We will replace three different values and obtain:

Now let's plot the three points on the coordinate system and connect them. This is actually the graph of the function for $y=2X$.