Verify the Point: Is (4, 19) on y = 2(x+6) - 1?

Q: Do I always substitute the x-coordinate first?

Yes! In function notation like $ y = f(x) $, you always substitute the x-value to find what the corresponding y-value should be.

Q: Can I work backwards from the y-value?

While you could substitute y = 19 and solve for x, the standard method is to substitute the x-coordinate first. This approach is more reliable and less prone to algebraic errors.

Q: Why is order of operations so important here?

Wrong order gives wrong answers! In $ y = 2(x+6)-1 $, you must do parentheses first: (4+6) = 10, then multiply by 2, then subtract 1. Skipping steps leads to incorrect verification.

Point Verification with Linear Functions

The point $(4,19)$ is located in the graph

$y=2(x+6)-1$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find if the point is on the line

00:03 In each point, the left number represents the X-axis and the right represents Y

00:12 Let's substitute the point in the line equation and see if it's possible

00:21 Always solve parentheses first

00:30 It's possible, therefore the point is on the line

00:34 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

The point $(4,19)$ is located in the graph

$y=2(x+6)-1$

Step-by-step solution

To solve this problem, we'll verify whether the point $(4, 19)$ lies on the graph of the function $y = 2(x + 6) - 1$ .

Substitute $x = 4$ into the function.
Calculate the resulting y-value.
Compare this y-value to 19 to determine if $(4, 19)$ is on the graph.

Let's perform these steps:

Step 1: Substitute $x = 4$ into the function:

$y = 2(4 + 6) - 1$

Step 2: Simplify the expression:

$y = 2 \times 10 - 1 = 20 - 1 = 19$

The calculated y-value is 19.

Step 3: Compare the calculated y-value with the y-coordinate of the point:

Since the calculated y-value (19) matches the y-coordinate of the point (19), the point $(4, 19)$ does indeed lie on the graph.

Thus, the answer is: Yes (the point lies on the graph).

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Rule: Substitute the x-coordinate into the function equation
Technique: Calculate: y = 2(4+6)-1 = 2(10)-1 = 19
Check: Compare calculated y-value with given y-coordinate ✓

Common Mistakes

Avoid these frequent errors

Not following order of operations when simplifying
Don't calculate 2(4+6)-1 as 2×4+6-1 = 13! This ignores parentheses and gives wrong results. Always follow PEMDAS: parentheses first, then multiplication, then subtraction.

Practice Quiz

Test your knowledge with interactive questions

Look at the linear function represented in the diagram.

When is the function positive?

FAQ

Everything you need to know about this question

What does it mean for a point to be 'on' a graph?

A point is on a graph when its coordinates satisfy the equation. This means when you substitute the x-value, you get exactly the same y-value as the point's y-coordinate!

Do I always substitute the x-coordinate first?

Yes! In function notation like $y = f(x)$ , you always substitute the x-value to find what the corresponding y-value should be.

What if my calculated y-value doesn't match?

If the calculated y-value is different from the given y-coordinate, then the point is not on the graph. For example, if we got y = 18 instead of 19, the answer would be No.

Can I work backwards from the y-value?

While you could substitute y = 19 and solve for x, the standard method is to substitute the x-coordinate first. This approach is more reliable and less prone to algebraic errors.

Why is order of operations so important here?

Wrong order gives wrong answers! In $y = 2(x+6)-1$ , you must do parentheses first: (4+6) = 10, then multiply by 2, then subtract 1. Skipping steps leads to incorrect verification.

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