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 $$ (1,2) $$.

Graphical Representation: Identifying the algebraic expression of a linear function

Question 1

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

Question 2

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

Question 3

Determine which of the following expressions describes a linear function?

Question 4

At what point does the graph intersect the x axis?

Question 5

At what point does the graph intersect the yaxis?

Examples with solutions for Graphical Representation: Identifying the algebraic expression of a linear function

Exercise #1

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

Video Solution

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 $(3,1)$ .

Exercise #2

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

Video Solution

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

$(4,2)$

Exercise #3

Determine which of the following expressions describes a linear function?

Video Solution

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

$y=4x+1$

Exercise #4

At what point does the graph intersect the x axis?

Video Solution

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.

Exercise #5

At what point does the graph intersect the yaxis?

Video Solution

Answer

$(0,2)$

Question 1

What representations describe a linear function?

Question 2

Which expressions represent linear functions and parallel lines?

Question 3

Which of the following represent linear functions and parallel lines?

Question 4

Which of the following describes linear functions and parallel lines?

Question 5

Which of the following describe linear functions?

Exercise #6

What representations describe a linear function?

Video Solution

Answer

Answers A + C are correct

Exercise #7

Which expressions represent linear functions and parallel lines?

Video Solution

Answer

Answers A+D are correct

Exercise #8

Which of the following represent linear functions and parallel lines?

Video Solution

Answer

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

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

Exercise #9

Which of the following describes linear functions and parallel lines?

Video Solution

Answer

_^$y=-4(x+1)$

_{^{$y=8x-12(x+1)$}}

Exercise #10

Which of the following describe linear functions?

Video Solution

Answer

Answers A and B are correct.

Question 1

Which of the following describes a linear function?

Question 2

$$ Choose representations describing linear functions and parallel lines.

Exercise #11

Which of the following describes a linear function?

Video Solution

Answer

Answers A and C are correct.

Exercise #12

Choose representations describing linear functions and parallel lines.

Video Solution

Answer

Las respuestas C y D son correctas