Graphical representation - Examples, Exercises and Solutions

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 y=ax+b .

The graphical representation of this function is a straight line that is ascending, descending, or parallel to the X X axis but never parallel to the Y 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 Y is isolated on one side and its coefficient is 1 1 )

A - Graphs of Direct Proportionality Functions

Suggested Topics to Practice in Advance

  1. Function
  2. Linear Function
  3. The Linear Function y=mx+b
  4. Positive and Negativity of a Linear Function
  5. Slope in the Function y=mx
  6. Finding a Linear Equation

Practice Graphical representation

examples with solutions for graphical representation

Exercise #1

A straight line has a slope of 6y and passes through the points (6,41) (6,41) .

Which function corresponds to the line described?

Video Solution

Step-by-Step Solution

To solve the exercise, we will start by placing the data we have into the equation of the line:
y = mx + b
41 = 6*6 + b
41 = 36 +b
41-36 = b
5 = b
 
Now we have the data for the equation of the straight line:
 
y = 6x + 5
But it still does not match any of the given options.

Keep in mind that a common factor can be excluded:
y = 2(3x + 2.5)

Answer

y=2(3x+212) y=2(3x+2\frac{1}{2})

Exercise #2

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

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Video Solution

Answer

(4,2) (4,2)

Exercise #3

At what point does the graph intersect the yaxis?

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Video Solution

Answer

(0,2) (0,2)

Exercise #4

At what point does the graph intersect the x axis?

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Video Solution

Answer

Does not cut the axis x

Exercise #5

What representations describe a linear function?

Video Solution

Answer

Answers A + C are correct

examples with solutions for graphical representation

Exercise #1

Which expression describes a linear function?

Video Solution

Answer

y=4x+1 y=4x+1

Exercise #2

Which expressions represent linear functions and parallel lines?

Video Solution

Answer

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

y=3+2x y=3+2x

Exercise #3

Which of the following represent linear functions and parallel lines?

Video Solution

Answer

y=12x+10 y=\frac{1}{2}x+10

y=12(x+2) y=\frac{1}{2}(x+2)

Exercise #4

Which of the following describes linear functions and parallel lines?

Video Solution

Answer

y=4(x+1) y=-4(x+1)

y=8x12(x+1) y=8x-12(x+1)

Exercise #5

Which statement is true according to the graph below?

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Video Solution

Answer

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

examples with solutions for graphical representation

Exercise #1

Does the first graph of the function pass through the origin of the axes?

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Video Solution

Answer

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

Exercise #2

Given the line parallel to the line y=4 y=4

and passes through the point (1,2) (1,2) .

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

Video Solution

Answer

y=2 y=2

Exercise #3

A straight line with a slope of 2y passes through the point (3,7) (3,7) .

Which equation corresponds to the line?

Video Solution

Answer

y=2x+1 y=2x+1

Exercise #4

Given the line parallel to the line y=2x+5 y=2x+5

and passes through the point (4,9) (4,9) .

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

Video Solution

Answer

y=2x+1 y=2x+1

Exercise #5

A straight line with the slope 9y passes through the point (5,8) (-5,-8) .

Which of the following equations corresponds to the line?

Video Solution

Answer

y=9x+37 y=9x+37

Topics learned in later sections

  1. Representation of Phenomena Using Linear Functions