### Home > AC > Chapter 6 > Lesson 6.2.4 > Problem6-74

6-74.

Identify the hypothesis and conclusion for each of the following statements. Then decide if the statement is true or false. Justify your decision. You may want to review the meanings of hypothesis and conclusion from problem 6-31.

1. If $y=\frac{2}{3}x-5$, then the point $(6,-1)$ is a solution.

Hypothesis:

Conclusion: $(6,−1)$ is a solution

Check to see if the conclusion is true by plugging in the points into the original equation.

2. If Figure 2 of a tile pattern has $13$ tiles and Figure 4 of the same pattern has $15$ tiles, then the pattern grows by $2$ tiles each figure.

Add $2$ tiles to Figure 2 to find figure three. Repeat the process to find Figure 4.
Does the number of tiles you found for Figure 4 match the number that the problem says there should be?

3. If $(3x+1)(x-2)=4$, then $3x^2-5x-2=4$.

Hypothesis: $(3x + 1)(x − 2) = 4$
Conclusion: $3x^² − 5x − 2 = 4$

Check by making a generic rectangle.
Does $(3x + 1)(x − 2) = 3x^² − 5x − 2$?