Finding the Positive Domain of a Linear Function with Slope 1.5

Given the function of the graph.

The slope is 1.5

What is the positive domain?

–16–16–16–14–14–14–12–12–12–10–10–10–8–8–8–6–6–6–4–4–4–2–2–2222444666888101010121212141414161616181818202020–10–10–10–8–8–8–6–6–6–4–4–4–2–2–2222444666888(0, -8)(0, -8)(0, -8)xy

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the negative domain of the function
00:07 Draw the function continuation until intersection with X-axis
00:19 Use the line equation to find intersection point with X-axis
00:24 Substitute appropriate values to find intersection point with X-axis
00:41 Isolate X
01:01 This is the intersection point with X-axis
01:08 And negative when the function is below X-axis
01:13 The function is positive when it's above X-axis
01:21 Identify when the function is positive and when negative
01:25 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the function of the graph.

The slope is 1.5

What is the positive domain?

–16–16–16–14–14–14–12–12–12–10–10–10–8–8–8–6–6–6–4–4–4–2–2–2222444666888101010121212141414161616181818202020–10–10–10–8–8–8–6–6–6–4–4–4–2–2–2222444666888(0, -8)(0, -8)(0, -8)xy

2

Step-by-step solution

To find the domain of positivity, we need to find the point of intersection of the equation with the x-axis.

For this, we need to find the formula of the equation.

We know that a linear equation is constructed as follows:

Y=MX+B

m represents the slope of the line, which is given to us: 1.5

b represents the point of intersection of the line with the Y-axis, which can be extracted from the existing point on the graph, -8.

And therefore:

Y=1.5X-8

Now, we replace:

Y=0, since we are trying to find the point of intersection with the X-axis.

0=1.5X-8
8=1.5X
5.3333 = X

We reveal that the point of intersection with the X-axis is five and one third (5.333)

Now, as we know that the slope is positive and the function is increasing, we can conclude that the domain of positivity is when the x values are less than five and one third.

That is:

5.333>X

And this is the solution!

3

Final Answer

513>x 5\frac{1}{3}>x

Practice Quiz

Test your knowledge with interactive questions

Look at the function shown in the figure.

When is the function positive?

xy-4-7

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