Find the Linear Equation: Line Negative When x < -2

Q: Why do all three equations work for this problem?

All three lines have positive slopes and cross the x-axis at x = -2. This means they're all negative when $ x and positive when \( x > -2 $.

Q: What does it mean for a line to be negative?

A line is negative when its y-values are below the x-axis (y

Q: Do I need to find where the line crosses the x-axis?

It helps! Set y = 0 and solve for x to find the x-intercept. For these equations, they all cross at x = -2, which explains why they're negative when x

Q: What if I get a positive result when testing?

If your test gives a positive y-value, that equation doesn't satisfy the condition. Double-check your arithmetic and make sure you picked an x-value that's actually less than -2.

Linear Equations with Sign Analysis

A line is negative in the domain

$x < -2$ .

Which equation represents the line?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the functions where the given negative domain is suitable

00:06 Find the intersection point with the X-axis

00:13 Isolate X

00:20 This is the intersection point with the X-axis

00:25 Let's draw the line

00:28 The line's slope is positive

00:36 We can see that this function is indeed suitable

00:41 Let's use the same method and check the following functions

00:47 Find the intersection point with the X-axis

01:00 This is the intersection point with the X-axis

01:03 Let's draw the line

01:07 The line's slope is positive

01:14 We can see that this function is indeed suitable

01:19 Let's use the same method and check the following functions

01:26 Find the intersection point with the X-axis

01:42 This is the intersection point with the X-axis

01:45 Let's draw the line

01:48 The line's slope is positive

01:54 We can see that this function is indeed suitable

02:03 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A line is negative in the domain

$x < -2$ .

Which equation represents the line?

Step-by-step solution

To determine which equation represents a line that is negative for $x < -2$ , we will evaluate each option by substituting $x = -3$ , which is less than -2:

For $y = 7x + 14$ : Substituting $x = -3$ , we have $y = 7(-3) + 14 = -21 + 14 = -7$ . This is negative, satisfying the condition.
For $y = 3x + 6$ : Substituting $x = -3$ , we have $y = 3(-3) + 6 = -9 + 6 = -3$ . This is also negative, meeting the requirement.
For $y = 1\frac{1}{2}x + 3$ : Substituting $x = -3$ , we have $y = 1.5(-3) + 3 = -4.5 + 3 = -1.5$ . Again, the result is negative.

All equations give negative values for $x < -2$ . Therefore, any of them represent a line that satisfies the given condition.

Hence, all answers are correct.

Final Answer

All answers are correct.

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Line is negative when y-values are below x-axis
Technique: Test x = -3: all equations give negative y-values
Check: Substitute test value less than -2 to confirm negative result ✓

Common Mistakes

Avoid these frequent errors

Testing only the boundary value x = -2
Don't substitute x = -2 to check if line is negative when x < -2 = gives zero or positive result! The boundary point doesn't tell you about the domain. Always test a value that's actually inside the given domain, like x = -3.

Practice Quiz

Test your knowledge with interactive questions

Look at the function shown in the figure.

When is the function positive?

FAQ

Everything you need to know about this question

Why do all three equations work for this problem?

All three lines have positive slopes and cross the x-axis at x = -2. This means they're all negative when $x < -2$ and positive when $x > -2$ .

How do I know which x-value to test?

Pick any value that satisfies the given condition! Since we need $x < -2$ , try x = -3, x = -5, or x = -10. They should all give negative y-values.

What does it mean for a line to be negative?

A line is negative when its y-values are below the x-axis (y < 0). This happens in certain intervals depending on the line's equation and where it crosses the x-axis.

Do I need to find where the line crosses the x-axis?

It helps! Set y = 0 and solve for x to find the x-intercept. For these equations, they all cross at x = -2, which explains why they're negative when x < -2.

What if I get a positive result when testing?

If your test gives a positive y-value, that equation doesn't satisfy the condition. Double-check your arithmetic and make sure you picked an x-value that's actually less than -2.

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Find the Linear Equation: Line Negative When x < -2

Linear Equations with Sign Analysis

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do all three equations work for this problem?

How do I know which x-value to test?

What does it mean for a line to be negative?

Do I need to find where the line crosses the x-axis?

What if I get a positive result when testing?

🌟 Unlock Your Math Potential

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