Classify the Linear Function: y=-5x+31 in Slope-Intercept Form

Q: How do I know if two lines are parallel just by looking at their equations?

Look at the slope (the coefficient of x)! If two lines have the same slope but different y-intercepts, they're parallel. For example: $ y = -5x + 31 $ and $ y = -5x + 3 $ both have slope -5.

Q: What does it mean when a function is decreasing?

A decreasing function means as x gets larger, y gets smaller. You can spot this when the slope is negative. Think of walking downhill from left to right!

Q: How do I find where a line crosses the y-axis?

The y-intercept is the constant term in $ y = mx + b $ form. It's the b value. For $ y = -5x + 31 $, the line crosses the y-axis at y = 31.

Q: Why do all the individual answers end up being correct?

Sometimes math problems test multiple properties of the same function! Here, we checked if the line is decreasing, parallel to another line, and passes through a specific point - and all three were true.

Q: Can two different functions have the same y-intercept?

Absolutely! Many different lines can cross the y-axis at the same point. They'll have different slopes but the same b value in $ y = mx + b $ form.

Linear Properties with Parallel Lines

Which of the following best describes the function below?

$y=-5x+31$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's choose the correct options together.

00:10 The function's coefficient is called the slope, and it shows us how the line tilts on the graph.

00:17 This graph is parallel to the other graph because their slopes are inverses of each other.

00:25 To find where the line crosses the Y-axis, we set X to zero and substitute it into the equation.

00:37 Here, we've found the intersection point with the Y-axis. Let's take a closer look.

00:43 Now, let's compare this intersection point with the one on the given graph.

00:49 We observe that both points match perfectly, which confirms our work.

00:58 The slope of the graph is negative, so we can say the function is decreasing over time.

01:04 Great job! And that's how we solve this problem.

Step-by-step written solution

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Understand the problem

Which of the following best describes the function below?

$y=-5x+31$

Step-by-step solution

The function $y = -5x + 31$ is analyzed as follows:

The slope of the function $y = -5x + 31$ is $-5$ , which is negative. This implies that the function is decreasing. Therefore, option 3 is correct.
The function $y = -5x + 31$ is in the form $y = mx + b$ , with a slope ( $m$ ) of $-5$ . The function $y = 3 - 5x$ can be rewritten as $y = -5x + 3$ , where the slope is also $-5$ . Hence, these two lines are parallel. Therefore, option 1 is correct.
The function $y = 2x + 31$ intersects the y-axis at $y = 31$ . The given function $y = -5x + 31$ also intersects the y-axis at $y = 31$ . Therefore, option 2 is correct.

Given that all individually assessed options are correct, the best answer is option 4: "All answers are correct."

Final Answer

All answers are correct.

Key Points to Remember

Essential concepts to master this topic

Slope: Negative slope indicates a decreasing function across all values
Parallel Lines: Functions with identical slopes like $m = -5$ are parallel
Y-intercept Check: At x = 0, both functions equal 31 ✓

Common Mistakes

Avoid these frequent errors

Confusing slope sign with function behavior
Don't assume positive slope means "correct" and negative means "wrong" = misunderstanding function direction! Negative slope simply means the line goes down from left to right. Always remember: negative slope = decreasing function, positive slope = increasing function.

Practice Quiz

Test your knowledge with interactive questions

What is the solution to the following inequality?

$$ 10x-4\leq-3x-8 $$

FAQ

Everything you need to know about this question

How do I know if two lines are parallel just by looking at their equations?

Look at the slope (the coefficient of x)! If two lines have the same slope but different y-intercepts, they're parallel. For example: $y = -5x + 31$ and $y = -5x + 3$ both have slope -5.

What does it mean when a function is decreasing?

A decreasing function means as x gets larger, y gets smaller. You can spot this when the slope is negative. Think of walking downhill from left to right!

How do I find where a line crosses the y-axis?

The y-intercept is the constant term in $y = mx + b$ form. It's the b value. For $y = -5x + 31$ , the line crosses the y-axis at y = 31.

Why do all the individual answers end up being correct?

Sometimes math problems test multiple properties of the same function! Here, we checked if the line is decreasing, parallel to another line, and passes through a specific point - and all three were true.

Can two different functions have the same y-intercept?

Absolutely! Many different lines can cross the y-axis at the same point. They'll have different slopes but the same b value in $y = mx + b$ form.

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Classify the Linear Function: y=-5x+31 in Slope-Intercept Form

Linear Properties with Parallel Lines

❤️ 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

How do I know if two lines are parallel just by looking at their equations?

What does it mean when a function is decreasing?

How do I find where a line crosses the y-axis?

Why do all the individual answers end up being correct?

Can two different functions have the same y-intercept?

🌟 Unlock Your Math Potential

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