Thread: equation and slope of lines

1. 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

2. 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.

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

They are negative reciprocals

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

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

now using the point and the slope we get

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

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.

3. 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 $\displaystyle (y - y_1) = m(x - x_1)$ 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.