Question

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

Answer 1

The absolute value of rate of change of both the equations are the same.

Explanation:

The first equation is
`y = - (1)/(4)x + 2` .......... (1)

This is a straight line equation in slope-intercept form and the slope of the straight line is
`- (1)/(4)` and y-intercept is at (0,2) i.e. y-intercept is 2 units.

Now, the second equation is
`2y = (1)/(2)x - 4`

⇒
`y = (1)/(4) x - 2` ........... (2)

This is again a straight line equation in slope-intercept form and the slope is
`(1)/(4)` and y-intercept is at (0,-2) i.e. y-intercept is - 2 units.

The equation (1) is decreasing function and equation (2) is an increasing function and the rate of decrease in (1) and the rate of increase in (2) are the same as the absolute value of slopes of those equations are the same. (Answer)