Question

Complete the table and answer the questions below.a) without graphing, which equation from above has the steepest line? How do you know?b) without graphing, which equation describes a decreasing line? How do you know?

Answer 1

The values on the table are:

$\begin{gathered} y=x-3 \\ \Rightarrow slope\colon m=1 \\ \Rightarrow y-axis\colon b=-3 \\ y=\frac{1}{5}x+2 \\ \Rightarrow slope\colon m=\frac{1}{5} \\ \Rightarrow y-axis\colon b=2 \\ y=-2x \\ \Rightarrow slope\colon m=-2 \\ \Rightarrow y-axis\colon b=0 \end{gathered}$

a) the steepest slope is m=-2 (from the third option). We can see this because in the first option, the rate of change is 1 and in the second option is 1/5. Then for each increase of x, the value of y will be modified but not as much as in the equation y=-2x.

b)the equation y=-2x represents a decreasing line, since the slope is negative.