Does the first graph of the function pass through the origin 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 graph is cut off at point $$ (1,2) $$

Graphical Representation: Identifying the algebraic expression of a linear function

Question 1

Does the first graph of the function pass through the origin 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

At what point does the graph intersect the x axis?

Question 4

Which expression describes a linear function?

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

Video Solution

Step-by-Step Solution

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

We'll highlight the point on the graph, and note that it doesn't lie on any of the plotted graphs.

Therefore, the answer is C. If we plot the point $(3,1)$ , we'll see that it lies on the first graph (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

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 touch the X-axis at all.

Therefore, the answer is D.

Answer

Does not cut the axis x

Exercise #4

Which expression 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.

Let's look at answer B and see that the formula indeed holds:

$y=mx+b$

Answer

$y=4x+1$

Exercise #5

At what point does the graph intersect the yaxis?

Video Solution

Answer

$(0,2)$

Question 1

Which expressions represent linear functions and parallel lines?

Question 2

What representations describe a linear function?

Question 3

Which of the following describes linear functions and parallel lines?

Question 4

Which of the following represent linear functions and parallel lines?

Question 5

Which of the following describe linear functions?

Exercise #6

Which expressions represent linear functions and parallel lines?

Video Solution

Answer

_$y=2(x+1)$

_$y=3+2x$

Exercise #7

What representations describe a linear function?

Video Solution

Answer

Answers A + C are correct

Exercise #8

Which of the following describes linear functions and parallel lines?

Video Solution

Answer

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

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

Exercise #9

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 #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