Which statement is true according to the graph below? 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 0 0 0

The graph intersects the x axis at the point $$ (4,0) $$.

The graph intersects the y axis at the point $$ (0,4) $$.

The graph passes through $$ (5,3) $$.

Does line I pass through the origin point of the axes? 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 –5 –5 –5 –4 –4 –4 –3 –3 –3 –2 –2 –2 –1 –1 –1 1 1 1 2 2 2 3 3 3 0 0 0 x y II I

Yes, it goes through $$ (0,0) $$.

No, it passes through $$ (3,2) $$.

No, the second line is cut off at point $$ (1,2) $$.

Which statement best describes the graph below? x y

The graph represents an ascending function.

The graph represents a decreasing function.

The graph represents a constant function.

Which of the following represent linear functions and parallel lines?

$$ y=\frac{1}{2}x+10 $$ $$ y=\frac{1}{2}(x+2) $$

Which expressions represent linear functions and parallel lines?

$$ y=2(x^2+1) $$ $$ y=2x^2+2 $$

Graphical Representation Practice Problems - Linear Functions

Master graphical representation of direct proportionality functions with step-by-step practice problems. Learn to identify slopes, y-intercepts, and graph linear equations.

📚Practice Graphing Linear Functions and Direct Proportionality

Graph linear functions using slope and y-intercept from y = ax + b
Identify ascending, descending, and horizontal lines from equation coefficients
Determine y-intercept points and their impact on graph position
Create value tables to plot accurate coordinate points
Recognize direct proportionality relationships in linear equations
Sketch graphs based on slope analysis and intersection points

Understanding Graphical Representation

Complete explanation with examples

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 $1$ )

A - Graphs of Direct Proportionality Functions

Detailed explanation

Practice Graphical Representation

Test your knowledge with 9 quizzes

Given the line parallel to the line $$ y=3x+4 $$

and passes through the point $(\frac{1}{2},1)$ .

Which of the algebraic representations is the corresponding one for the given line?

Examples with solutions for Graphical Representation

Step-by-step solutions included

Exercise #1

Which statement is true according to the graph below?

Step-by-Step Solution

If we plot all the points, we'll notice that point $(3,5)$ is the correct one, because:

$x=3,y=5$

And they intersect exactly on the line where the graph passes.

Answer:

The graph passes through $(3,5)$ .

Video Solution

Exercise #2

Does line I pass through the origin point of the axes?

Step-by-Step Solution

Let's first remember that the origin of the coordinate system is $(0,0)$ .

We'll highlight the point on the graph, noting that it doesn't lie on any of the plotted lines.

Therefore, the answer is C; If we plot the point $(3,1)$ , then we'll see that it lies on line I (the blue one).

Answer:

No, it passes through $(3,1)$ .

Video Solution

Exercise #3

At which point does the graph of the first function (I) intersect the graph of the second function (II)?

Step-by-Step Solution

Let's pay attention to the point where the lines intersect. We'll mark it.

We'll find that:

$X=4,Y=2$

Therefore, the point is:

$(4,2)$

Answer:

$(4,2)$

Video Solution

Exercise #4

Determine which of the following expressions describes a linear function?

Step-by-Step Solution

Note that in answer A there is an exponent, therefore the answer is incorrect.

Note that in answer C, if we multiply X by X we get X to a power, therefore the answer is incorrect.

Note that in answer D there is an exponent, therefore the answer is incorrect.

In answer B the following formula can be observed.

$y=mx+b$

Answer:

$y=4x+1$

Video Solution

Exercise #5

At what point does the graph intersect the x axis?

Step-by-Step Solution

Note that the line intersects only the Y-axis. In other words, it does not go through the X-axis at all.

Therefore, the answer is (d).

Answer:

It does not intersect the x axis.

Video Solution

Frequently Asked Questions

Everything you need to know about Graphical Representation

How do you graph a linear function from its equation?

To graph a linear function y = ax + b, first identify the slope (a) and y-intercept (b). Plot the y-intercept point on the y-axis, then use the slope to find additional points by moving right 1 unit and up/down according to the slope value.

What does the slope tell you about a line's direction?

The slope coefficient determines line direction: when a > 0, the line ascends from left to right; when a < 0, the line descends; when a = 0, the line is horizontal and parallel to the x-axis.

How do you find where a line crosses the y-axis?

The y-intercept is the coefficient b in the equation y = ax + b. This tells you exactly where the line crosses the y-axis at point (0, b). If b is positive, it crosses above the origin; if negative, below the origin.

What is direct proportionality in linear functions?

Direct proportionality occurs when y = ax (where b = 0), meaning the line passes through the origin. For every unit increase in x, y increases by a constant factor of 'a', creating a straight line through (0,0).

How do you create a table of values for graphing?

Choose several x-values (like -2, -1, 0, 1, 2), substitute each into your equation y = ax + b, calculate the corresponding y-values, then plot these coordinate pairs (x,y) on your graph and connect them with a straight line.

Can a linear function line be vertical?

No, linear functions of the form y = ax + b cannot be vertical lines. Vertical lines are parallel to the y-axis and cannot be expressed as functions since they fail the vertical line test (one x-value would have multiple y-values).

What's the difference between positive and negative slopes in graphs?

Positive slopes (a > 0) create ascending lines that rise from left to right, while negative slopes (a < 0) create descending lines that fall from left to right. The steeper the absolute value of the slope, the more dramatic the rise or fall.

How do you identify direct proportionality from a graph?

A graph represents direct proportionality when the line passes through the origin (0,0) and maintains a constant slope. This creates a straight line where the ratio of y to x remains constant for all points on the line.

Continue Your Math Journey

Master Graphical Representation first, then advance to these related topics that build on your fraction skills

Topics Learned in Later Sections

Representation of Phenomena Using Linear Functions

Practice by Question Type

Choose your preferred learning style and practice format for fraction problems

Determining the slope of a function with a point Finding points on the graph of a function Identifying and reading the graph of a linear function Identifying the algebraic expression of a linear function Using additional geometric shapes

Graphical Representation Practice Problems - Linear Functions

Understanding Graphical Representation

Practice Graphical Representation

Examples with solutions for Graphical Representation

Frequently Asked Questions

How do you graph a linear function from its equation?

What does the slope tell you about a line's direction?

How do you find where a line crosses the y-axis?

What is direct proportionality in linear functions?

How do you create a table of values for graphing?

Can a linear function line be vertical?

What's the difference between positive and negative slopes in graphs?

How do you identify direct proportionality from a graph?

More Graphical Representation Questions