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# Module 5 topic 2

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### Module 5 topic 2

1. 1. Module 5 Topic 2 <br />Parallel and Perpendicular Slopes<br />
2. 2. Example 1<br />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?<br />Remember that perpendicular slopes are the opposite reciprocals so if we have 3 then the opposite reciprocal would be -1/3<br />
3. 3. Example 2<br />Similar Problem: If you are finding the line parallel to the graph of x + 4y = 7, what is the slope of the line?<br />x + 4y = 7 (solve for y)<br />4y = -x + 7<br />y = -x/4 + 7/4<br />remember that -x/4 the slope is -1/4 so the parallel slope is also -1/4 <br />
4. 4. Example 3<br />Similar Problem: If you are finding the line parallel to the graph of x + 4y = 7, what is the slope of the line?<br />x + 4y = 7 (solve for y)<br />4y = -x + 7<br />y = -x/4 + 7/4<br />remember that -x/4 the slope is -1/4 so the perpendicular slope is the opposite reciprocal which would be 4/1 or 4 <br />
5. 5. Example 4<br />Similar Problem: Write the slope-intercept equation of the line perpendicular to y = 7/2 x - 2, which passes through the point (0, 3).<br />y = 7/2 x - 2 (the slope is 7/2 so the perpendicular slope is -2/7)<br />Use the perpendicular slope and the ordered pair to find b in y = mx + b.<br />y= mx + b<br />0 = -2/7(3) + b<br />0 = -6/7 + b<br />6/7 = b<br />so the equation of the line perpendicular would be y = -2/7x + 6/7<br />
6. 6. Example 5<br />Similar Problem: Write the slope-intercept form of the equation parallel to<br />y= 8x + 3, which passes through (2, -5).<br />y= 8x + 3 (the slope is 3 so the parallel slope is also 3)<br />Use the parallel slope and the ordered pair to find the line of the equation.<br />y= mx + b<br />-5 = 3(2) + b<br />-5 = 6 + b<br />-11 = b<br />y= 3x - 11 is the line parallel to the equation y = 3x + 8.<br />
7. 7. Example 6<br />Similar Problem: Write the equation of a line parallel to the line y = 8, that passes through the point (2, 7).<br />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.<br />So in this case it is y = 7.<br />
8. 8. Example 7<br />Similar Problem: Write the equation of a line perpendicular to the line y = 8, that passes through the point (2, 7).<br />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.<br />So in this case it is x = 2.<br />

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