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1# Find the equation of the line parallel to y = 6x + 10 passing through (-3, 9).

2# Find the equation of the line perpendicular to y= 2/3x + 6 passing through (5, -2).

the point-slope form for a line is the best place to start for problems like these, since they give you a point and a slope.

#1 y-9 = 6(x+3)
#2 y+2 = -3/2 (x-5)

Did you know?

Did you know that when you are looking for the equation of a line parallel to another line, the slopes of the two lines are always equal? In the first example, the line parallel to y = 6x + 10 and passing through (-3, 9) will have the same slope of 6. Using this information, you can find the equation of the new line. Similarly, did you know that when you are looking for the equation of a line perpendicular to another line, the slopes of the two lines are always negative reciprocals of each other? In the second example, the line perpendicular to y= (2/3)x + 6 and passing through (5, -2) will have a slope of -3/2 (-2/3 flipped and negated). With this slope, you can find the equation of the perpendicular line. Understanding these concepts can help you solve problems involving parallel and perpendicular lines!