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Chapter 2: Q. 2 (page 76)

True or False: The point -2,-6is on the graph of the equationx=2y-2.

Short Answer

Expert verified

The statement is false.

Step by step solution

01

Step 1. Given information

Need to check whether the statement "The point -2,-6is on the graph of the equation x=2y-2." is true or false.

02

Step 2. Check

For the point-2,-6, need to check whether x=-2and y=-6satisfies the equation x=2y-2or not.

x=2y-2-2=2-6-2-2=-12-2-2=-14

But -2≠-14.

Therefore, the equation is not satisfied.

03

Step 3. Final answer

The equation is not satisfied, so the point -2,-6is not on the graph.

Therefore, the given statement "The point -2,-6is on the graph of the equation x=2y-2" is false.

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Most popular questions from this chapter

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.

h(x)=-x33x2-9

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

f(x)=x2-1

A semicircle of radius r is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle. See the figure.

(a) Express the area A of the rectangle as a function of the radius r of the semicircle.

(b) Express the perimeter p of the rectangle as a function of r.

A wire of length xis bent into the shape of a square.

Part (a): Express the perimeter pof the square as a function of x.

Part (b): Express the area Aof the square as a function of x.

Write the point–slope form of the line with slope 5 containing the point (3, -2).
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