Verify if the points (1,-2), (3,6), and (5,10) lie on the line y=2x.
Understand the Problem
The question is asking whether the given points (1, -2), (3, 6), and (5, 10) satisfy the equation of the line y = 2x. We will check if each point, when substituted into the equation, will result in a true statement.
Answer
The points (3, 6) and (5, 10) satisfy the equation $y = 2x$.
Answer for screen readers
The points (3, 6) and (5, 10) satisfy the equation $y = 2x$, while (1, -2) does not.
Steps to Solve
- Substituting the first point (1, -2)
Substitute $x = 1$ and $y = -2$ into the equation $y = 2x$.
$$ -2 = 2(1) $$
Calculate the right side:
$$ -2 = 2 $$
This statement is false.
- Substituting the second point (3, 6)
Now, substitute $x = 3$ and $y = 6$ into the equation $y = 2x$.
$$ 6 = 2(3) $$
Calculate the right side:
$$ 6 = 6 $$
This statement is true.
- Substituting the third point (5, 10)
Finally, substitute $x = 5$ and $y = 10$ into the equation $y = 2x$.
$$ 10 = 2(5) $$
Calculate the right side:
$$ 10 = 10 $$
This statement is true.
- Conclusion Determine which points satisfy the equation. Only the points (3, 6) and (5, 10) satisfy the equation $y = 2x$. The point (1, -2) does not satisfy the equation.
The points (3, 6) and (5, 10) satisfy the equation $y = 2x$, while (1, -2) does not.
More Information
In this problem, we evaluated whether given points lie on the line described by the equation $y = 2x$. A point lies on the line if substituting its coordinates into the equation yields a true statement.
Tips
- A common mistake is forgetting to check both $x$ and $y$ values when substituting into the equation. Ensure both coordinates are verified against the equation.
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