# Thread: Help!!!! Slope-Intercept Form

1. ## Help!!!! Slope-Intercept Form

1. Find the slope and y-intercept of 5x - 2y = 3.

2. Indicate which of the following sets of lines are parallel, perpendicular, or neither. Show your work.
(a) y = 2x - 5
y = 2x + 5

(b) 3x + y = 5
-x + 3x = 6

(c) 3x + y =5
x + y = 3

I really need help! Please explain to me how to find the answers to these problems. Thanks for any help you can give me!

2. Originally Posted by alwaysalillost
1. Find the slope and y-intercept of 5x - 2y = 3.
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

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 parallel if they have the same slope (or gradient)
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

(b) 3x + y = 5
-x + 3x = 6
the first line is:
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?

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

3. Originally Posted by Jhevon
the first line is:
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?
Sorry about that...you are right. I wrote it wrong.

3x + y = 5
-x + 3y = 6

Thanks!

4. Originally Posted by alwaysalillost
Sorry about that...you are right. I wrote it wrong.

3x + y = 5
-x + 3y = 6
3x + y = 5
-x + 3y = 6

the first line is:
3x + y = 5
=> y = -3x + 5 ----------> slope = -3

the second line is:
-x + 3y = 6
=> 3y = x + 6
=> y = (1/3)x + 2 -------> slope = 1/3

since the slopes are negative inverses of each other, the two lines are perpendicular