Parallel Lines
|Parallel Lines SAME SLOPE |1. A highway is being built parallel to the train tracks. The equation |
| |of the line for the tracks is [pic], what is the slope of the highway? |
|Perpendicular Lines OPPOSITE RECIPROCAL (change the sign and |A. 3/7 B. 7/3 C. -3/7 D. -7/3 |
|flip the fraction) | |
|Ex: -5 ( [pic] Ex: [pic] ( [pic] |2. The equation of a line containing one side of a parallelogram is |
|To find slope the equation must be in slope intercept form |[pic]. The opposite side contains the point (5, -4). What is the |
|[pic] (solve for y) |equation of the line that contains the opposite side? |
|Ex: Find slope of 7x – 3y = 9 |A. y = 2/5 x – 6 B. y = -2/5 x – 4 |
|-3y = -7x + 9 (subtract 7x) |C. y = -2/5 x – 2 D. y = 2/5x – 3 |
|y = 7/3 x – 3 (divide by -3) | |
|Slope is 7/3. |3. Line m is parallel to line n and passes through (5, -7). If the |
|Slope of parallel is 7/3 |equation of n is y=-3/5x + 2, which describes m? |
|Slope of perpendicular is -3/7 |line m has a slope of -3/5 and a y-intercept of -4 |
|Use given information (read the questions carefully!): Look |line m has a slope of -3/5 and a y-intercept of -7 |
|at the answer choices because some can be eliminated if slope|line m has a slope of -3/5 and a y-intercept of 2 |
|is not the same (parallel) or opposite reciprocal. Then |line m has a slope of 5/3 and a y-intercept of -4 |
|graph the answer choices, look at the table and look for the| |
|point it goes through or the y-intercept. |4. Which is an equation of a line parallel to [pic] |
| | |
|Special Cases |A. y = 2x + 3 |
|Vertical lines have a slope that is undefined | |
|Ex: x=3 |C. y = 1/2x + 2 |
|Horizontal lines have zero slope | |
|Ex: y=-2 | |
| |B. y = -2x + 4 |
|Changing Variables in an equation: | |
|Plug in correct numbers for the variables |D. y = -1/2x + 4 |
|Graph the equation | |
|Change the number(s). | |
|Then look at the new graph. |5. Which is an equation of a line that is perpendicular to the line |
|Ex: Consider the equation y = mx + b in which m < 0 and b > |graphed in question number 4? |
|0. What happens to the x-intercept if b increases and m |A. y = 2x + 3 B. y = -2x + 3 |
|remains the same? |C. y = ½ x + 1 D. y = -1/2x – 1 |
|So let m be -2 and b be 4. | |
|The graph crosses the x-axis at 2. |6. First street is perpendicular to L street. The equation |
|Now increase b to be 6 and keep m at -2 |of L street on a map is represented by the equation |
|The graph now crosses the x-axis at 3 |y =2x + 6. What is the equation representing |
|The answer is: x-intercept increases |First Street if it passes through the point (4,5)? |
| | |
| |A. y = -2x - 3 B. y = -2x + 5 C. y = 1/2x + 7 D. y =1/2 x+ 5 |
| | |
| |6 7. Line q passes through (6,4) and is perpendicular to the graph of|
| |the line y= -2/3x +8. Which is the equation of line q? |
| |A. |
| |y = -2/3x + 8 |
| |B. |
| |y = 3/2x + 5 |
| | |
|Midpoint of (x1, y1) and (x2, y2) |C. |
|[pic] |y = 2/3x |
|Calculator: x 1 + x2 ENTER / 2 |D. |
|y1 + y2 ENTER / 2 |y = 3/2 x – 5 |
|(The average of the x’s and the average of the y’s) | |
| | |
|Ex: Find the midpoint of [pic] |8. Given points A(7,8), B(5,-2) C(6,-8) and D(8,10) which of the |
|[pic] |following is true? |
|Or: 3 + -4 ENTER / 2 and 2 + 1 ENTER /2 |A. [pic] is parallel to [pic] B. [pic] is parallel to |
| |[pic] |
|!!! Read question carefully, sometimes you are given midpoint|C. [pic] is perpendicular to [pic] D. None of these are true |
|!!! |9. Consider the line y = mx + b where m>0 and b>0. What change occurs |
| |if m is multiplied by -1 and the |
|Ex: If the midpoint of [pic] is [pic]Find the missing |x-intercept remains the same? |
|coordinate. |A. The y-intercept becomes positive. |
|Do the following: |B. The y-intercept becomes negative. |
|1) Plug in each answer choice OR |C. The slope becomes positive. |
|2) Graph the midpoint and the known point and try to figure |D. The y-intercept remains the same. |
|out where the other point is. OR | |
|3) Set up the midpoint formula using given information. |10. Consider the line y = mx + b where m>0 and b>0. Suppose that the |
|[pic] |x-intercept is increased and the slope remains the same. What happens |
|Only focus on the coordinate with the variable. Set = to |to the y-intercept? |
|midpoint coordinate [pic] What can you add to -2 that will |A. It moves up. B. It moves down. |
|average to 2? |C. It moves right. D. It moves left |
|Solve. -2+x=4 | |
|X=6 |11. On a map, Sarah’s house is located at (-4, 6) and Jose’s house is |
|Distance [pic] |located at (13, 7). What point is exactly halfway in between Sarah and |
|[pic] |Jose? |
|Calculator: [pic] |A. (-2.5, 9.5) B. (-11,5) C. (30, 8) D. (4.5,6.5) |
|Ex: Find the distance between [pic]Plug in numbers | |
|[pic] |12. Points A and B have a midpoint M. A is |
|OR [pic]= 9.06 |(9, 1) and M is (5, 3). Find the coordinates of B? |
|Read question carefully, sometimes you are given distance and|A. (7,2) B. (13, -1) C. (1, 5) D. (11.5, 2.5) |
|must plug in your answer choices. | |
| |13. Points P (5,7) and Q(-3,9) are the enpoints of a diameter of a |
| |circle. What are the coordinates of point O, the center of the circle?|
| |A. (1,8) B. (-1,8) C. (3.5,11.5) D. (-11,11) |
| | |
| |14. The library is directly between the Post Office and the local bank.|
| |The library is 3 blocks east and 2 blocks south of the center of town. |
| |The Post Office is 1 block east and 4 blocks north of the center of |
| |town. Find the location of the local bank from the center of town. |
| |A. 2 blocks east, 2 blocks north |
| |B. 3 ½ blocks east, 0 blocks north |
| |C. 1 block west, 8 blocks south |
| |D. 5 blocks east, 8 blocks south |
| | |
| |15. The coordinates of a square are (-3, -6), (3, 2), |
| |(0, 5), (12,11). Find the area. (Round answer to the nearest tenth.) |
| |16. Find the perimeter of the triangle with points |
| |(-5, 3), (4, 2), (7, -1). Round answer to nearest tenth. |
| | |
| |17. What is the length between (-4, -5) and (5, 2)? |
| |(Round the answer to the nearest tenth) |
| | |
| |18. The distance between school and your house is [pic] miles. If your |
| |house is located at (10, 1), find a missing coordinate of school (x, |
| |8). |
| |A. 3 B. 11 C. 8 D. 50 |
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