2. Example 1 Similar Problem: If line one has a slope of 3, what does the slope of line 2 need to be if the lines are perpendicular? Remember that perpendicular slopes are the opposite reciprocals so if we have 3 then the opposite reciprocal would be -1/3
3. Example 2 Similar Problem: If you are finding the line parallel to the graph of x + 4y = 7, what is the slope of the line? x + 4y = 7 (solve for y) 4y = -x + 7 y = -x/4 + 7/4 remember that -x/4 the slope is -1/4 so the parallel slope is also -1/4
4. Example 3 Similar Problem: If you are finding the line parallel to the graph of x + 4y = 7, what is the slope of the line? x + 4y = 7 (solve for y) 4y = -x + 7 y = -x/4 + 7/4 remember that -x/4 the slope is -1/4 so the perpendicular slope is the opposite reciprocal which would be 4/1 or 4
5. Example 4 Similar Problem: Write the slope-intercept equation of the line perpendicular to y = 7/2 x - 2, which passes through the point (0, 3). y = 7/2 x - 2 (the slope is 7/2 so the perpendicular slope is -2/7) Use the perpendicular slope and the ordered pair to find b in y = mx + b. y= mx + b 0 = -2/7(3) + b 0 = -6/7 + b 6/7 = b so the equation of the line perpendicular would be y = -2/7x + 6/7
6. Example 5 Similar Problem: Write the slope-intercept form of the equation parallel to y= 8x + 3, which passes through (2, -5). y= 8x + 3 (the slope is 3 so the parallel slope is also 3) Use the parallel slope and the ordered pair to find the line of the equation. y= mx + b -5 = 3(2) + b -5 = 6 + b -11 = b y= 3x - 11 is the line parallel to the equation y = 3x + 8.
7. Example 6 Similar Problem: Write the equation of a line parallel to the line y = 8, that passes through the point (2, 7). Hint: If a line is equal to y and have no x-value then the line parallel is the y-value of the ordered pair. So in this case it is y = 7.
8. Example 7 Similar Problem: Write the equation of a line perpendicular to the line y = 8, that passes through the point (2, 7). Hint: If a line is equal to y and have no x-value then the line perpendicular is the is the x-value of the ordered pair. So in this case it is x = 2.
