Discover Points on Line y=2x+1: A Journey Through Coordinates

Q: Why can't I just look at the graph to find points?

Graphing can be imprecise and lead to estimation errors! The algebraic method of substitution gives you exact verification. Always use the equation to confirm points.

Q: What if I get a different y-value than the coordinate shows?

That means the point does not lie on the line! For example, when x = 3, we get $ y = 2(3) + 1 = 7 $, but (3,10) has y = 10, so it's not on the line.

Q: Do I need to check every answer choice?

For multiple choice questions, yes! Check each option systematically. Even if you find one correct answer, verify the others are wrong to be completely sure.

Q: What does it mean when a point 'passes through' the function?

It means the point lies exactly on the line represented by the function. The coordinates must satisfy the equation perfectly when substituted.

Linear Function Verification with Point Substitution

$y=2x+1$

Through which points does the function above pass?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find out which points are on the line.

00:08 Each point has an X value and a Y value. The X is first. The Y is second.

00:14 We'll plug each point into the line equation to check if it fits.

00:19 No fit means the point is not on the line.

00:23 Use this method for all points to find which ones are on the line.

00:37 No fit, so this point is not on the line.

00:43 Let's check this point next.

00:54 No fit again, so not on the line.

00:59 Let's try the next point.

01:12 This point fits, so it's on the line.

01:16 And that's how we find points on the line!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$y=2x+1$

Through which points does the function above pass?

Step-by-step solution

To find which point lies on the graph of the function $y = 2x + 1$ , we will substitute the $x$ values from each choice and see if the output $y$ matches the $y$ of that point.

Let's evaluate each point:

For $(0,0)$ : Substitute $x = 0$ into $y = 2x + 1$ , we get $y = 2(0) + 1 = 1$ . Does not match $y = 0$ .
For $(3,10)$ : Substitute $x = 3$ into $y = 2x + 1$ , we get $y = 2(3) + 1 = 7$ . Does not match $y = 10$ .
For $(5,12)$ : Substitute $x = 5$ into $y = 2x + 1$ , we get $y = 2(5) + 1 = 11$ . Does not match $y = 12$ .
For $(4,9)$ : Substitute $x = 4$ into $y = 2x + 1$ , we get $y = 2(4) + 1 = 9$ . Matches $y = 9$ .

Therefore, the point through which the function $y = 2x + 1$ passes is $(4,9)$ .

Final Answer

$(4,9)$

Key Points to Remember

Essential concepts to master this topic

Substitution Rule: Replace x with coordinate's x-value in the equation
Technique: Calculate $y = 2(4) + 1 = 9$ to verify point (4,9)
Check: Compare calculated y-value with given coordinate's y-value for match ✓

Common Mistakes

Avoid these frequent errors

Assuming points are on the line without verification
Don't just guess or assume points lie on $y = 2x + 1$ = wrong answers guaranteed! Visual estimation fails with linear functions. Always substitute each x-coordinate into the equation and verify the y-value matches exactly.

Practice Quiz

Test your knowledge with interactive questions

Which statement best describes the graph below?

FAQ

Everything you need to know about this question

Why can't I just look at the graph to find points?

Graphing can be imprecise and lead to estimation errors! The algebraic method of substitution gives you exact verification. Always use the equation to confirm points.

What if I get a different y-value than the coordinate shows?

That means the point does not lie on the line! For example, when x = 3, we get $y = 2(3) + 1 = 7$ , but (3,10) has y = 10, so it's not on the line.

Do I need to check every answer choice?

For multiple choice questions, yes! Check each option systematically. Even if you find one correct answer, verify the others are wrong to be completely sure.

How do I substitute correctly?

Replace the variable x with the number from the coordinate. For point (4,9): substitute x = 4 into $y = 2x + 1$ to get $y = 2(4) + 1$ .

What does it mean when a point 'passes through' the function?

It means the point lies exactly on the line represented by the function. The coordinates must satisfy the equation perfectly when substituted.

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