# The Point-Slope form of the equation of a line

#### hazlecheerbabe

##### New member
OK so im new on here so im just gonna tell you the problem:
Find the slope of a line that is (a)Parallel to the line with the given equation: and (b)Perpendicular to the line with the given equation.
y=3x
I know that you can add a zero an that will make it in slope intercept form but i thought you had to have a slope an two points to do the point-slope form???? HELP!
Y=1/4X-5

#### mmm4444bot

##### Super Moderator
Staff member

The instructions ask only for slopes, not equations.

y = 3x

y = (1/4)x - 5

Both of these equations are in slope-intercept form. (We do not need to actually write the zero on the first one; we understand that it's there.)

The y-intercept has nothing to do with the slope. You can read off the slope from both of these equations because they are both in slope-intercept form. Doing this gives you the answers for part (a).

Lines parallel to these two have the same slope as each.

Do you know what the relationship is between slopes of perpendicular lines? This knowledge gives you the answers for part (b).

The point-slope form of the equation for a line is not needed for the exercise that you posted.

However, a line is determined by a single point and a slope. You do not need two points to determine a line once you know its slope.

If you do not know the slope, then two points are needed to determine a line.

Do you know enough to find the slope of the lines given by the two equations above?

If you need more help, then please post whatever work or reasoning that you're able to do so far.

#### Loren

##### Senior Member
y=mx+b

m is the slope of the line. b is the y-intercept.

So, if b is not given, b=0 and the line crosses the y axis at y=0 which is the origin.

Two parallel lines have the same slope.

The slopes of two perpendicular lines are the negative reciprocals of each other. For instance, if the slope of line[sub:q218sevy]1[/sub:q218sevy] is 5 then the slope of a line perpendicular to line[sub:q218sevy]1[/sub:q218sevy] is -1/5.