# Graphical Representation of a Function that Represents Direct Proportionality

🏆Practice graphical representation

The graphical representation of a function that represents direct proportionality is actually the ability to express an algebraic expression through a graph. Since it's a direct proportionality, the graph will be that of a straight line.

The graphical representation of a function that represents direct proportionality is actually the ability to express an algebraic expression through a graph.

As it is a direct proportionality, the graph will be of a straight line.

A function that represents direct proportionality is a linear function of the family $y=ax+b$.

The graphical representation of this function is a straight line that is ascending, descending, or parallel to the $X$ axis but never parallel to the $Y$ axis.

Note: we observe the line from left to right.

We can now recognize in the equation of the line what the graphical representation of each function looks like:

(only when the equation is explicit $Y$ is isolated on one side and its coefficient is $1$)

## Test yourself on graphical representation!

Which statement is true according to the graph below?

## A -> the slope of the line

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 point of intersection with the Y-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 $b$.

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## Examples of Graphical Representation of a Linear Function

### Example 1 (use of the graph)

$y=5x-4$
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.

### Example 2 (using the table)

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 $y=2X$.

Do you know what the answer is?
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