On Amber’s math test, she was asked whether the equation y=1/2y^2 represents a function. She made the following table and graph.
2 answers:
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Answer:
Step-by-step explanation:
Remember that:
- Two lines are parallel if their slopes are the same.
- Two lines are perpendicular if their slopes are negative reciprocals.
- And two lines are neither (a.k.a intersecting) if they are neither parallel nor perpendicular.
We want to find the value of x such that .
Therefore, the slopes of BC and DE must be equivalent.
So, let's find the slope of BC first.
BC)
We can use the slope formula:
Let B(17, 5) be (x₁, y₁) and let C(11, -3) be (x₂, y₂). Substitute:
Subtract:
So, the slope of BC is 4/3.
DE)
Let D(-1, 2) be (x₁, y₁) and let E(x, -6) be (x, y₂). Substitute:
We know that the two slopes must be equal. So, the slope of DE must also be 4/3. Substitute 4/3 for m:
Solve for x. Simplify the right:
Cross multiply:
Multiply on the right:
Divide both sides by 4:
Subtract 1 from both sides:
So, the value of x is -7.
And we're done!