Y-intercepts and lines going perpendicular to others

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elisemd

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Jan 3, 2006
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Back in the day, I was not taught very well about linear equations and what they would look like if they went parallel or perpendicular to other lines. Can you please help me figure out how to do this problem?

Problem: Find the y-intercept of the linear equation passing through the points (3,-2) and perpendicular to the line -3x+6y=2.
a. -4
b. -8
c. 4
d. -1/2
e. 1/2
f. -7/2
g. 8

Now, I don't want someone to just say that its a or c or something. I really want to know HOW you get to the answer. Please help. Thank you.

~Elise
 
elisemd said:
Back in the day, I was not taught very well about linear equations and what they would look like if they went parallel or perpendicular to other lines. Can you please help me figure out how to do this problem?

Problem: Find the y-intercept of the linear equation passing through the points (3,-2) and perpendicular to the line -3x+6y=2.
a. -4
b. -8
c. 4
d. -1/2
e. 1/2
f. -7/2
g. 8

Now, I don't want someone to just say that its a or c or something. I really want to know HOW you get to the answer. Please help. Thank you.

~Elise
Click to expand...

If two (non-horizontal or vertical) lines are perpendicular, then their slopes are opposite reciprocals.

So, you need to start by finding the slope of the given line,
-3x + 6y = 2
You can solve the equation for y to get the equation in slope-intercept form:
6y = 3x + 2
y = (3/6)x + (2/6)
y = (1/2)x + (1/3)

The slope of this line is 1/2, and any line perpendicular to this one will have a slope of -2/1, or -2.

You can begin to write the equation of the line, since we now know the slope:
y = -2x + b

Next, we know that this line passes through the point (3, -2). Substitute 3 for x and -2 for y:
-2 = -2(3) + b
-2 = -6 + b
4 = b

Ok...now we know the equation of the line:
y = -2x + 4

You should be able to tell the y-intercept of this line very easily.
 
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