Question

Y = -1/4x + 2 and 2y = 1/2x - 4
how do these lines compare?

Answer 1

the line 1 has negative slope of -1/4 and line 2 has positive slope of 1/4.

Explanation:

let the line 1 be y = -1/4x + 2 and line 2 be 2y = 1/2x - 4

these lines are in the form of y = mx + c

where m is the slope of the line and c is the intercept made with y axis.

dividing the line 2 by 2 we get
`y = (1)/(4)x -2`

line 1 meets x axis when y = 0 applying y = 0 in equation 1 we get x = 8

line 2 meets x axis when y=0 applying y = 0 in equation 2 we get x = 8

line 1 meets y axis when x = 0 applying x= 0in equation 1 we get y = 2

line 2 meets y axis when x = 0 applying x= 0in equation 2 we get y = -2

therefore line 1 passes through (8,0)and (0,2) with negative slope of -1/4

and line 2 passes through (8,0) and (0,-2) with positive slope of 1/4.