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.
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.