I have to determine which two equations represent parallel lines.

equations are
(a) y=(-4)x+2
(b) y=(4)x+2
(c) y= (1/2)x +2
(d) y=(-4)x+3

so the answer would be:

A and D

yes

To determine which two equations represent parallel lines, we need to compare the slopes of the equations.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope.

Comparing the given equations, we can see that equations (a) and (d) have the same slope of -4. Therefore, these two equations represent parallel lines.

Equation (b) has a slope of 4, which is the negative reciprocal of -4. So, it is not parallel to equations (a) and (d).

Equation (c) has a slope of 1/2, which is also not parallel to equations (a) and (d).

Hence, the equations representing parallel lines are A (y = (-4)x + 2) and D (y = (-4)x + 3).