(-1,-2) and (3, -162) a. Is there a line th(at goes through these two points? How do you know? If there is one, what is the equation of the line going through these two points? if there isn't one, explain why not.

Answer:The equation of line for given points is y = - 40 x - 42  Step-by-step explanation:Given two points as :( -1 , - 2 )  and ( 3 , - 162 )Now, Equation of line in points form y - [tex]y_1[/tex] = m × ( x -  [tex]x_1[/tex] )Where m is the slope of lineAnd, m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]or, m = [tex]\frac{ - 162 + 2}{ 3 + 1}[/tex]or, m =  [tex]\frac{ - 160}{ 4}[/tex]∴   m = - 40So, Slope of line for given points is - 40Now equation of line can be written as y - ( - 2 ) = ( - 40 ) × ( x -  ( - 1 ) )or, y + 2 =  ( - 40 ) × ( x + 1 )or, y + 2 = - 40 x - 40or, y = - 40 x - 40 - 2∴  y = - 40 x - 42        Hence the equation of line for given points is y = - 40 x - 42    Answer