# equation and slope of lines

• May 11th 2008, 09:37 AM
jsimms
equation and slope of lines
Find the equation of each line. Write each answer in slope intercept form.

1.) The line goes through (1,2) and is perpendicular to y=1/2x-3

2.) The line goes through (2,3) and is parallel to -2x+y=6
• May 11th 2008, 09:44 AM
TheEmptySet
Quote:

Originally Posted by jsimms
Find the equation of each line. Write each answer in slope intercept form.

1.) The line goes through (1,2) and is perpendicular to y=1/2x-3

2.) The line goes through (2,3) and is parallel to -2x+y=6

How are the slopes of perpendicular lines related.

$m_2=\frac{-1}{m_1}$

They are negative reciprocals

the negative reciprocal of 1/2 is -2 or using the above formlua

$m_2=\frac{-1}{\frac{1}{2}}=-2$

now using the point and the slope we get

$y-2=-2(x-1) \iff y-2=-2x+2 \iff y=-2x+4$

If lines are parallel they have the same slope.

Try putting the above line in y=mx+b form.

I hope this helps.

Good luck.
• May 11th 2008, 12:51 PM
masters
Parallel Lines have same slope
In response to your second situation, note that parallel lines have the same slope.

Therefore, -2x + y = 6 is equivalent to y = 2x + 6. The slope (m) = 2

Use point-slope form again $(y - y_1) = m(x - x_1)$ with (2, 3) and m = 2, we have:

(y - 3) = 2(x - 2)

You may want to convert this one to y =mx + b or ax + by = c.