Consider the line y=-5/7x-7 Find the equations of the line that is perpendicular & parallel to this line and passes through the points (-7,5)
your equation : y = -5/7x - 7 In this form, y = mx + b, m is your slope. So your slope in this equation is -5/7. For a parallel line, the slope stays the same, so it is -5/7. Now we sub that into this formula : y - y1 = m(x - x1) (-7,5) x1 = -7 and y1 = 5 now lets sub y - 5 = -5/7(x - (-7) y - 5 = -5/7(x + 7) y - 5 = -5/7x - 35/7 -- add 5 to both sides y = -5/7x - 35/7 + 5 y = -5/7x - 35/7 + 35/7 y = -5/7x ==> this is your parallel line To find the perpendicular line, we will need the negative reciprocal of the slope of the equation. All that means is " flip " the slope and change the sign. The slope was -5/7. Your perpendicular slope will be 7/5 (you see how I flipped the slope and changed the sign.) now we will use y - y1 = m(x - x1) slope(m) = 7/5 (-7,5) x1 = -7 and y1 = 5 now lets sub y - 5 = 7/5(x - (-7) y - 5 = 7/5(x + 7) y - 5 = 7/5x + 49/5 -- add 5 to both sides y = 7/5x + 49/5 + 5 y = 7/5x + 49/5 + 25/5 y = 7/5x + 74/5 ==> this is your perpendicular line
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