Which statement is true according to the graph below?111222333444555666777111222333444555666777888000

The graph intersects the x axis at the point $ (4,0) $.

The graph intersects the y axis at the point $ (0,4) $.

The graph passes through $ (5,3) $.

Linear Function Analysis: Interpreting Slope on Coordinate Plane

Q: How do I read coordinates from a graph accurately?

Start at the origin (0,0). Move right for positive x-values, then up for positive y-values. Remember: x comes first in (x,y), so go right first, then up!

Q: What if the line seems to pass close to a point but not exactly through it?

In math, close doesn't count! The line must pass exactly through the point. If it's even slightly off, that point is not on the line.

Q: What's the difference between 'passes through' and 'intersects'?

'Passes through' means the line goes exactly through that point anywhere on the graph. 'Intersects' usually refers to where the line crosses the x-axis or y-axis specifically.

Linear Function Point Verification with Coordinate Analysis

Which statement is true according to the graph below?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the correct answer

00:03 Let's check all points according to X and Y axis coordinates

00:06 On the left is the X-axis, and on the right is the Y-axis

00:10 This point is not on the line

00:15 We'll use this method for all points, and check which ones are on the line

00:46 Only this point is on the line

00:53 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 statement is true according to the graph below?

Step-by-step solution

If we plot all the points, we'll notice that point $(3,5)$ is the correct one, because:

$x=3,y=5$

And they intersect exactly on the line where the graph passes.

Final Answer

The graph passes through $(3,5)$ .

Key Points to Remember

Essential concepts to master this topic

Graph Reading: Identify the exact x and y coordinates where the line passes
Technique: Check if point (3,5) lies on the line by locating x=3, y=5
Verification: Trace vertical line from x=3 to meet horizontal line from y=5 ✓

Common Mistakes

Avoid these frequent errors

Confusing x and y coordinates
Don't read (3,5) as x=5, y=3 or mix up the order! This flips the coordinates and makes you check the wrong point. Always remember the first number is x (horizontal) and second is y (vertical).

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 do I read coordinates from a graph accurately?

Start at the origin (0,0). Move right for positive x-values, then up for positive y-values. Remember: x comes first in (x,y), so go right first, then up!

What if the line seems to pass close to a point but not exactly through it?

In math, close doesn't count! The line must pass exactly through the point. If it's even slightly off, that point is not on the line.

How can I tell if (3,5) or (5,3) is correct without guessing?

Look at the graph systematically! Find x=3 on the horizontal axis, trace up to the line, then check what y-value you hit. Do the same for x=5. Only one will match exactly.

Why do some answer choices mention intercepts?

Intercepts are special points where the line crosses the axes. The x-intercept has y=0, and the y-intercept has x=0. These are common but not the only important points on a line!

What's the difference between 'passes through' and 'intersects'?

'Passes through' means the line goes exactly through that point anywhere on the graph. 'Intersects' usually refers to where the line crosses the x-axis or y-axis specifically.

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