Question

1. complete the following table for the lines shown:

lines	how are they similar?	how are they different?

how are they similar?	how are they different?

Explanation:

Step1: Analyze slope - intercept form

The equation of line A is $y = x + 2$, and line B is $y=-3x$. For linear equations $y = mx + b$ (where $m$ is slope and $b$ is y - intercept).

Step2: Find similarities

Both are linear equations of the form $y=mx + b$ (for line A $m = 1,b = 2$; for line B $m=-3,b = 0$). They are straight - line graphs in a two - dimensional coordinate system.

Step3: Find differences

The slope of line A is $m_A=1$ (a positive slope, so it rises from left to right), and the slope of line B is $m_B=-3$ (a negative slope, so it falls from left to right). Also, the y - intercept of line A is 2 ($y(0)=2$) and the y - intercept of line B is 0 ($y(0)=0$).

Answer:

Similar: Both are linear functions represented as straight lines on a coordinate plane.
Different: Line A has a positive slope ($m = 1$) and y - intercept of 2, while line B has a negative slope ($m=-3$) and y - intercept of 0.