Identify the Function of Line 1: Graph Analysis in Coordinate Plane

Q: How can I tell if a line has positive or negative slope just by looking?

Use the "left to right" rule! If the line goes up from left to right, the slope is positive. If it goes down from left to right, the slope is negative. Line 1 clearly goes down, so it has negative slope.

Q: Why does the line going through the origin matter?

When a line passes through the origin (0,0), it means the y-intercept is zero. This simplifies the equation to $ y = mx $ instead of $ y = mx + b $.

Q: Could line 1 be y = -6x instead of y = -x?

Look at the steepness! A line with slope -6 would be much steeper, dropping 6 units down for every 1 unit right. Line 1 appears to drop 1 unit down for every 1 unit right, indicating slope = -1.

Q: What's the difference between y = x and y = -x on a graph?

$ y = x $ creates a line going up from left to right (positive slope), while $ y = -x $ creates a line going down from left to right (negative slope). They're mirror images across the x-axis!

Linear Function Identification with Slope Analysis

Which function describes the line numbered 1?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Match the function to line 1

00:04 The function is decreasing, therefore the slope is negative

00:09 Let's eliminate all functions with positive slope

00:17 Let's substitute a specific point in each function and find it on the graph

00:37 According to the graph, we'll match it to the function

00:45 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

Which function describes the line numbered 1?

Step-by-step solution

To solve this problem, we'll follow these steps:

Determine if the given line labeled '1' has a positive or negative slope.
Find out if the line passes through the origin, which implies the y-intercept, $b = 0$ .
Identify the function equation based on the observations.

Now, let's work through each step:
- Observation shows that line '1' in red goes through the origin (intersects at the point (0,0)), confirming that the y-intercept, $b$ , is zero.
- Given that this line descends from left to right, the slope $m$ is negative. Therefore, the most likely function representation given the described visual descent is $y = -x$ .

Thus, the function describing the line numbered '1' is $y = -x$ .

Final Answer

$y=-x$

Key Points to Remember

Essential concepts to master this topic

Slope Direction: Line descending left to right indicates negative slope
Origin Test: Line passes through (0,0) means y-intercept b = 0
Verification: Check that $y = -x$ gives negative y for positive x ✓

Common Mistakes

Avoid these frequent errors

Confusing slope direction with equation sign
Don't assume a line going down means y = x with a negative answer! A line descending from left to right has negative slope, so the equation itself contains the negative: y = -x. Always identify slope direction first, then write the equation correctly.

Practice Quiz

Test your knowledge with interactive questions

For the function in front of you, the slope is?

FAQ

Everything you need to know about this question

How can I tell if a line has positive or negative slope just by looking?

Use the "left to right" rule! If the line goes up from left to right, the slope is positive. If it goes down from left to right, the slope is negative. Line 1 clearly goes down, so it has negative slope.

Why does the line going through the origin matter?

When a line passes through the origin (0,0), it means the y-intercept is zero. This simplifies the equation to $y = mx$ instead of $y = mx + b$ .

Could line 1 be y = -6x instead of y = -x?

Look at the steepness! A line with slope -6 would be much steeper, dropping 6 units down for every 1 unit right. Line 1 appears to drop 1 unit down for every 1 unit right, indicating slope = -1.

How do I check if y = -x is correct for this graph?

Pick any point on line 1 and test it! For example, if the line passes through (2, -2), substitute: -2 = -(2) = -2 ✓. The equation works!

What's the difference between y = x and y = -x on a graph?

$y = x$ creates a line going up from left to right (positive slope), while $y = -x$ creates a line going down from left to right (negative slope). They're mirror images across the x-axis!

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