Question

Are `y=2/3x-2` and `y=3/2x+1` parallel to each other?

Answer 1

No, they are not parallel because they have different slopes.

See full explanation below.

Explanation:

Parallel lines have the same slope.

You can determine the slope of a line if it is in slope-intercept form, which both of these equations are.

The slope-intercept form of a linear equation is:

`y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b` is the y-intercept value.

Equation 1) `y = color(red)(2/3)x - color(blue)(2)`

Equation 2) `y = color(red)(3/2)x + color(blue)(1)`

The slope of the first equation is `m = color(red)(2/3)` and the slope of the second equation is `m = color(red)(3/2)`, They are not equal and therefore they are not parallel.