Positivity and Negativity: Finding a linear equation using positive and negative domains

Examples with solutions for Positivity and Negativity: Finding a linear equation using positive and negative domains

Exercise #1

Which equation represents a line that is positive in domain for each value of x.

Video Solution

Step-by-Step Solution

To find out if the equation intersects the x-axis, we need to substitute y=0 in each equation.
If the function has a solution where y=0 then the equation has an intersection point and is not the correct answer.

 

Let's start with the first equation:

y = 3x+8

We will substitute as instructed:

0 = 3x+8

3x = -8

x = -8/3

Although the result here is not a "nice" number, we see that we are able to arrive at a result and therefore this answer is rejected.

 

Let's move on to the second equation:

y = 300x+50

Here too we will substitute:

0 = 300x + 50
-50 = 300x

-50/300 = x
-1/6 = x

In this exercise too we managed to arrive at a result and therefore the answer is rejected.

 

Let's move on to answer C:

y = 3

We will substitute:

0 = 3

We see that here an impossible result is obtained because 0 can never be equal to 3.

Therefore, we understand that the equation in answer C is the one that does not intersect the x-axis, and is in fact positive all the time.

 

Therefore answer D is also rejected, and only answer C is correct.

Answer

y=3 y=3

Exercise #2

Choose the equation that represents a line with a negative domain of 0 < x .

Video Solution

Answer

y=2x y=-2x

Exercise #3

Choose the equation that represents a straight line that is positive in the domain 8 > x

and passes through the point (0,9) (0,9) .

Video Solution

Answer

y=118x+9 y=-1\frac{1}{8}x+9

Exercise #4

Given the function is negative in the domain 4 > x

Find the equation of the line given that it passes through the point (5,9) (5,9)

Video Solution

Answer

y=9x36 y=9x-36

Exercise #5

A line is negative in the domain

x < -2 .

Which equation represents the line?

Video Solution

Answer

All answers are correct.

Exercise #6

Given a function that is positive from the beginning of the axes. Plus the point (7,9) on the graph of the function. Find the equation for the function.

Video Solution

Answer

y=127x y=1\frac{2}{7}x

Exercise #7

Which function is positive in the domain below?

-7 > x

Video Solution

Answer

y=3x21 y=-3x-21

Exercise #8

Choose the functions that fit the following description:

The function is positive in the domain 2 < x .

a. y=3x+4 y=3x+4

b. y=2x4 y=2x-4

c. y=2x+4 y=-2x+4

d. y=2 y=2

e. y=4x8 y=4x-8

f. y=5x14 y=5x-14

Video Solution

Answer

a, b, d, e

Exercise #9

Given a function that is negative in the domain 4 < x only.

Moreover, its point of intersection with the y axis is (0,12) (0,-12)

Find the equation daxis iscribing the line.

Video Solution

Answer

No solution

Exercise #10

The following is a function that is positive in domain:

3 < x

Choose the equation that describes it given that the absolute value of the slope is 2.

Video Solution

Answer

y=2x6 y=2x-6