when the equation of a line is written in the form, y = mx + b, m is the slope, and b is the y-intercept. so we have,

5x - 2y = 3

=> 2y = 5x - 3

=> y = (5/2)x - 3/2

so the slope is 5/2 and the y-intercept is -3/2

two lines are parallel if they have the same slope (or gradient)

2. Indicate which of the following sets of lines are parallel, perpendicular, or neither. Show your work.

(a) y = 2x - 5

y = 2x + 5

two lines are perpendicular if there slopes are negative inverses of each other. that is, if two lines are perpendicular and the slope of one is m, then the slope of the other is -1/m. example. if the slope of a line is 2, then the slope of the line perpendicular to it is -1/2

so we have,

y = 2x - 5

y = 2x + 5

these lines are parallel, since both have a slope of 2, there is no work to show

the first line is:(b) 3x + y = 5

-x + 3x = 6

3x + y = 5

=> y = -3x + 5 ----------> slope = -3

the second line is:

hold on, you have two x's here, which should be the y?

the first line is:(c) 3x + y =5

x + y = 3

3x + y = 5

=> y = -3x + 5 ------------> slope = -3

the second line is:

x + y = 3

=> y = -x + 3 -------------> slope = -1

since -3 not= -1

and -3 not= 1/1

the lines are neither perpendicular nor parallel