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

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Which statement best describes the graph below?

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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