Graph Intersection: Points on the Line y=2(x+2)-1

Q: Do I need to simplify the equation first or can I use the original form?

You can use either form, but simplifying to $ y = 2x + 3 $ makes calculations much easier! It's the same line, just written more simply.

Q: What if I get the wrong y-value when I substitute?

That means the point doesn't lie on the line! Only points where your calculated y-value exactly matches the given y-coordinate are on the function.

Q: How do I check if (5,13) is correct?

Substitute x = 5: $ y = 2(5) + 3 = 13 $. Since this matches the y-coordinate 13, the point (5,13) is on the line!

Q: Why don't the other points work?

Let's check (0,0): $ y = 2(0) + 3 = 3 $, not 0. For (10,13): $ y = 2(10) + 3 = 23 $, not 13. The calculated y-values don't match the given coordinates.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find which points are on the line

00:03 Open parentheses properly, multiply by each factor

00:11 This is the equation of the line

00:15 In each point, the left number represents the X-axis and the right represents Y

00:19 Let's substitute each point in the line equation and see if it's possible

00:27 Not possible, therefore the point is not on the line

00:32 We'll use the same method for all points to find which ones are on the line

00:35 Let's move to this point

00:47 Not possible, therefore the point is not on the line

01:06 Possible, therefore the point is on the line

01:12 Let's move to this point

01:21 Not possible, therefore the point is not on the line

01:25 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

Through which points does the function below pass?

$y=2(x+2)-1$

2

Step-by-step solution

To determine through which points the function $y = 2(x+2) - 1$ passes, let's proceed methodically.

Step 1: Simplify the expression of the linear function:

The given function is $y = 2(x+2) - 1$ . Distribute the $2$ over the terms inside the parenthesis:
$y = 2x + 4 - 1$

Simplify further by combining like terms:
$y = 2x + 3$

Step 2: Evaluate the function at different $x$ -values to find which points lie on the line represented by the function $y = 2x + 3$ .

Step 3: Check each of the provided choice points:

For choice $(0,0)$ : Substituting $x = 0$ into $y = 2x + 3$ , we get $y = 2(0) + 3 = 3$ . This does not match $y = 0$ .
For choice $(10,13)$ : Substituting $x = 10$ into $y = 2x + 3$ , we get $y = 2(10) + 3 = 23$ . This does not match $y = 13$ .
For choice $(5,13)$ : Substituting $x = 5$ into $y = 2x + 3$ , we get $y = 2(5) + 3 = 13$ . This matches $y = 13$ , so this point lies on the line.
For choice $(4,13)$ : Substituting $x = 4$ into $y = 2x + 3$ , we get $y = 2(4) + 3 = 11$ . This does not match $y = 13$ .

Therefore, the point through which the given function passes is $(5,13)$ .

3

Final Answer

$(5,13)$

Key Points to Remember

Essential concepts to master this topic

Simplification: Distribute and combine like terms to get standard form
Substitution: Replace x with given value: y = 2(5) + 3 = 13
Verification: Check if calculated y-value matches given coordinate ✓

Common Mistakes

Avoid these frequent errors

Using original form without simplifying first
Don't substitute directly into y = 2(x+2) - 1 without distributing = harder calculations and more errors! This makes checking points unnecessarily complex. Always simplify to y = 2x + 3 first for easier substitution.

Practice Quiz

Test your knowledge with interactive questions

Which statement best describes the graph below?

FAQ

Everything you need to know about this question

Do I need to simplify the equation first or can I use the original form?

+

You can use either form, but simplifying to $y = 2x + 3$ makes calculations much easier! It's the same line, just written more simply.

What if I get the wrong y-value when I substitute?

+

That means the point doesn't lie on the line! Only points where your calculated y-value exactly matches the given y-coordinate are on the function.

How do I check if (5,13) is correct?

+

Substitute x = 5: $y = 2(5) + 3 = 13$ . Since this matches the y-coordinate 13, the point (5,13) is on the line!

Why don't the other points work?

+

Let's check (0,0): $y = 2(0) + 3 = 3$ , not 0. For (10,13): $y = 2(10) + 3 = 23$ , not 13. The calculated y-values don't match the given coordinates.

Can a line pass through more than one of these points?

+

A straight line can pass through multiple points, but in this case, only (5,13) satisfies the equation. The other points would be on different lines with different slopes or y-intercepts.

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Graph Intersection: Points on the Line y=2(x+2)-1

Linear Functions with Point Verification

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