Question

Plato math help please

Answer 1

Answer: option (C)

Step-by-step explanation: The slope of a linear function is undetermined when the line is parallel respect to the y-axis. In the current problem there is no way to observe such geometrical issue, but if we consider how to derive the slope using the following expression;
`m=(\Delta y)/(\Delta x)= (y_(2)-y_(1))/(x_2-x_(1))`.

With the previous equation, we have

`a) for P_(1)(-1,1), P_(2)(1,-1)   m=(\Delta y)/(\Delta x)= (-1-1)/(1-(1))=(-2)/(2)=1\\`, therefore the slope is defined

`b) for P_(1)(-2,2), P_(2)(2,2)   m=(\Delta y)/(\Delta x)= (2-2)/(2-(2))=(0)/(4)=0\\`, therefore the slope is defined

`c) for P_(1)(-3,3), P_(2)(-3,3)   m=(\Delta y)/(\Delta x)= (3-(-3))/(-3-(-3))=(6)/(0)=undetermined\\`

`d) for P_(1)(-4,4), P_(2)(4,4)   m=(\Delta y)/(\Delta x)= (4-(-4))/(4-(-4))=(8)/(8)=1\\`

In this case, the option (C) shows that is not possible to divide over zero. Given such issue, the slope is undetermined and therefore it is a vertical line parallel to y-axis.