Analyzing Function y=2x-3: Is It Increasing or Decreasing?

Linear Functions with Slope Analysis

Given the following function:

$y=2x-3$

Is the function increasing or decreasing?

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Step-by-step video solution

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00:00 Is the function increasing or decreasing?

00:03 Is the function increasing or decreasing?

00:07 The function's slope is positive according to the given data

00:12 When the function's slope is positive, the function is increasing

00:16 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 following function:

$y=2x-3$

Is the function increasing or decreasing?

2

Step-by-step solution

To determine whether the function $y = 2x - 3$ is increasing or decreasing, we need to analyze the slope of the linear function.

We start by identifying the equation given: $y = 2x - 3$ .

This equation is in the standard linear form, $y = mx + b$ , where:
$m$ is the slope, and
$b$ is the y-intercept.

The slope $m$ in this equation is $2$ . In the context of linear functions:

If $m > 0$ , the function is increasing.
If $m < 0$ , the function is decreasing.
If $m = 0$ , the function is constant (neither increasing nor decreasing).

In our function, the slope $m = 2$ , which is greater than zero. Therefore, we can conclude that the function $y = 2x - 3$ is increasing.

As a result, the function is increasing.

3

Final Answer

Increasing

Key Points to Remember

Essential concepts to master this topic

Slope Rule: Positive slope means increasing, negative slope means decreasing
Technique: Identify m in $y = mx + b$ : here m = 2
Check: Test two points: when x increases, y increases too ✓

Common Mistakes

Avoid these frequent errors

Confusing y-intercept with slope
Don't look at the -3 and think the function is decreasing = wrong conclusion! The -3 is just where the line crosses the y-axis. Always focus on the coefficient of x (the slope) to determine if a function increases or decreases.

Practice Quiz

Test your knowledge with interactive questions

Is the function in the graph decreasing?

FAQ

Everything you need to know about this question

How do I remember which way is increasing vs decreasing?

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Think of walking uphill vs downhill! If the slope is positive, you're walking uphill (increasing). If negative, you're walking downhill (decreasing). For $y = 2x - 3$ , the slope is +2, so it's uphill!

What does the -3 do if it doesn't affect increasing/decreasing?

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The -3 is the y-intercept - it just moves the entire line up or down on the graph. It doesn't change the direction the line is going, only where it starts on the y-axis.

Can I test points to check if a function is increasing?

+

Yes! Pick any two x-values where the first is smaller. If the corresponding y-values also get larger, the function is increasing. For example: when x = 0, y = -3; when x = 1, y = -1. Since -1 > -3, it's increasing!

What if the slope was exactly 0?

+

If the slope equals zero, like $y = 0x + 5$ or just $y = 5$ , then the function is constant - neither increasing nor decreasing. It's a horizontal line!

Does a steeper positive slope mean it increases faster?

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Exactly! A slope of +5 increases faster than +2, and +2 increases faster than +0.5. The bigger the positive number, the steeper the upward climb.

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