Make a Conjecture

Zefram analyzed a linear relationship, found that the slope-intercept equation was \(\text{y} = 3.5\text{x} + 16\), and made a prediction for the value of y for a given value of x. He realized that he made an error calculating the y-intercept and that it was actually 12. Can he just subtract 4 from his prediction if he knows that the slope is correct? Explain.

Communicate Mathematical Ideas

The table shows a linear relationship. How can you predict the value of y when x = 6 without finding the equation of the relationship?

Critique Reasoning

Louis says that if the differences between the values of x are constant between all the points on a graph, then the relationship is linear. Do you agree? Explain.

Make a Conjecture

Suppose you know the slope of a linear relationship and one of the points that its graph passes through. How could you predict another point that falls on the graph of the line?

Explain the Error

Thomas used (7, 17.5) and (18, 45) from a graph to find the equation of a linear relationship as shown. What was his mistake?

\(\begin{align}
\text{m} &= \frac{45-7}{18-17.5} = \frac{38}{0.5} = 79 \\
\text{y} &= 79\text{x} + \text{b}\\
49 &= 79\times18 + \text{b} \\
45 &= 1422 + \text{b},\text{ so b } = -1337\\
&\text{The equation is y } = 79\text{x} - 1377\\
\end{align}
\)