Does line I pass through the origin point of the axes?111222333444555666777–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333000xyIII

Yes, it goes through $ (0,0) $.

No, it passes through $ (3,2) $.

No, the second line is cut off at point $ (1,2) $.

Linear Functions Analysis: Does Function I Pass Through the Origin?

Q: How can I tell if a line passes through the origin just by looking at the graph?

Visually trace the line back to where x = 0. If the line crosses the y-axis at y = 0, then it passes through the origin $ (0,0) $. If it crosses above or below, it doesn't pass through the origin.

Q: What's the difference between lines that pass through the origin and those that don't?

Lines through the origin have equations like y = mx (no added number). Lines that don't pass through the origin have equations like y = mx + b where b ≠ 0.

Q: How do I identify specific points on a line from the graph?

Find where the line intersects grid lines. In this case, line I clearly passes through the point $ (3,1) $ where x = 3 and y = 1 meet on the grid.

Q: What if the graph is hard to read exactly?

Look for points where the line crosses grid intersections - these give you exact coordinates. Use these clear points rather than trying to estimate unclear areas of the graph.

Linear Functions with Graph Interpretation

Does line I pass through the origin point of the axes?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Does graph 1 pass through the origin?

00:02 The origin is the point (0,0)

00:05 We can see that the line does not pass through it

00:08 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

Does line I pass through the origin point of the axes?

Step-by-step solution

Let's first remember that the origin of the coordinate system is $(0,0)$ .

We'll highlight the point on the graph, noting that it doesn't lie on any of the plotted lines.

Therefore, the answer is C; If we plot the point $(3,1)$ , then we'll see that it lies on line I (the blue one).

Final Answer

No, it passes through $(3,1)$ .

Key Points to Remember

Essential concepts to master this topic

Origin Definition: The origin is the point where x-axis and y-axis intersect $(0,0)$
Visual Check: Trace line I to see if it passes through $(0,0)$ or another point
Verification: Line I passes through $(3,1)$ instead of the origin ✓

Common Mistakes

Avoid these frequent errors

Assuming diagonal lines always pass through origin
Don't assume that all slanted lines pass through $(0,0)$ = wrong identification! Only lines with equation y = mx (no y-intercept) pass through the origin. Always trace the line back to see where it crosses the y-axis.

Practice Quiz

Test your knowledge with interactive questions

Which statement best describes the graph below?

FAQ

Everything you need to know about this question

How can I tell if a line passes through the origin just by looking at the graph?

Visually trace the line back to where x = 0. If the line crosses the y-axis at y = 0, then it passes through the origin $(0,0)$ . If it crosses above or below, it doesn't pass through the origin.

What's the difference between lines that pass through the origin and those that don't?

Lines through the origin have equations like y = mx (no added number). Lines that don't pass through the origin have equations like y = mx + b where b ≠ 0.

Why doesn't line I pass through the origin in this graph?

Looking at the graph, line I (the blue line) crosses the y-axis above the origin. When you trace it to x = 0, it intersects at approximately $(0, 1)$ , not $(0,0)$ .

How do I identify specific points on a line from the graph?

Find where the line intersects grid lines. In this case, line I clearly passes through the point $(3,1)$ where x = 3 and y = 1 meet on the grid.

What if the graph is hard to read exactly?

Look for points where the line crosses grid intersections - these give you exact coordinates. Use these clear points rather than trying to estimate unclear areas of the graph.

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