IM 8.4.8 Practice: How Many Solutions?

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GeoGebra Classroom Activities, IM 6 – 8 Math

Lin was looking at the equation . She said, “I can tell right away there are no solutions, because on the left side, you will have and a bunch of constants, but you have just on the right side.” Do you agree with Lin? Explain your reasoning.

Han was looking at the equation . He said, “I can tell right away there are no solutions, because on the left side, you will have  and a bunch of constants, but you have just on the right side.” Do you agree with Han? Explain your reasoning.

Decide whether each equation is true for all, one, or no values of x.

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Select all that apply
  • A
  • B
  • C
Check my answer (3)

Solve each of these equations. Explain or show your reasoning.

The points  and are each on the graph of a linear equation. Is also on the graph of this linear equation? Explain your reasoning.

In the picture triangle  is an image of triangle  after a rotation. The center of rotation is . What is the length of side ? Explain how you know.

What is the measure of angle ? Explain how you know.

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