Parallel and Perpendicular

This week I am to find the equation of a line that is parallel or perpendicular to given lines that pass through specific point.
The given equation y=12 x+3
The parallel line must pass through point (-2, 1)
Parallel lines share the same slope so the slope of the new line will be12. Because I have an ordered pair and the slope, I can use point-slope to find the new equation

Y-y1=m(x-x1) Standard point-slope form y-1=12(x-(-2)) Slope and ordered pair substituted into the equation y-1=12(x) +-12(2) simplified double negatives and distributed slope y= 12x+2 the equation of the parallel line
When two lines are parallel they both share the same slope but they never cross at any point on the graph
This line rises from left to right. The y-intercept is 2 units above the origin and the x-intercept is 4 units to the left of the origin.
When two lines are perpendicular to one another the slope of the perpendicular line will be the negative reciprocal of the other and they will cross each other at only 1 point.
The equation given y=34x-1
The perpendicular line must pass through the point (4, 0)
The slope given is34. The negative reciprocal will be -43. Using the given ordered pair I will again use point-slope to find the equation of the line perpendicular to the given line
Y-y1=m(x-x1) Standard point-slope form y-0=-43(x-4) Slope and ordered pair substituted into the equation y=-43x+163 the equation of the perpendicular line
This line falls across the graph from the left to the right. The y-intercept is 16/3 units above the origin, and the x-intercept is 4 units to the right of the