Practice with Slopes and  Equations of  Lines Topic Index | Geometry Index | Regents Exam Prep Center

 Answer the following questions dealing with slopes and equations of lines.
 1. Which of the following equations passes through the points (2,4) and (-3,-6)? Choose: y = (1/2)x - 2 y = 2x y = 2x + 4 y = (-1/2)x + 2 Explanation Find the slope first.  (4+6)/(2+3) = 2 Using the point (2,4) [you could also use (-3,-6)] y-4 = 2(x-2) y-4 = 2x-4 y = 2x

 2. What is the slope of a line perpendicular to 2y = -6x - 10? Choose: -3   3 -1/3   1/3 Explanation The slope of the given line is -3. The negative reciprocal for the perpendicular is 1/3.

 3. Given 3y - 4x = 5 and  4y + 6 = 3x. Are these lines parallel, perpendicular or neither? Choose: parallel perpendicular neither Explanation The slope of the first line is 4/3. The slope of the second line is 3/4. Neither. We are missing the negation to be perpendicular.

 4. What is the equation of a line that passes through the point (4,-5) and is parallel to 3x + 2y = 12? Choose: y = -3x + 6 y = (3/2)x + 1 y = 3x + 1 y = (-3/2)x + 1 Explanation The slope of the given line is -3/2. Parallels have equal slopes. The new line y + 5 = (-3/2)(x - 4) y + 5 = (-3/2)x + 6 y = (-3/2)x + 1

 5. What is the equation of a line that passes through the point (-1,-2) and is perpendicular to -5x = 6y + 18? Choose: y = (6/5)x - (4/5) y = (-6/5)x + (6/5) y = (6/5)x + (4/5) y = (-6/5)x - (4/5) Explanation slope of the given line is (-5/6). Slope of perpendicular is 6/5. y + 2 = (6/5) (x + 1)

6.

 x 1 3 5 7 y 2 5 8 11

A line passes through the points shown in this table.
What is the slope of a line perpendicular to this line?

Choose:

3/2
-2/3
-3/2
2/3

 7. Given 4y - 2x = 10 and  -6y - 6 = -3x. Are these lines parallel, perpendicular or neither? Choose: parallel perpendicular neither Explanation The slope of both lines is 1/2. Slope being equal means parallel.

 8. What is the equation of a line that is parallel to y = -4 and passes through the point (3,7)? Choose: y = 3x - 4 y = 3 y = 3x + 7 y = 7 Explanation The slope of y = -4 is zero and the line is horizontal. Lines parallel will also be horizontal. A horizontal line through (3,7) is y = 7.

 9. Write the equation of a line that is parallel to 4x + 2y = -8 and has the same y-intercept as -3y = -2x - 9? Choose: y =  4x - 9 y = -4x - 9 y = -2x - 3 y = -2x + 3 Explanation Vertical lines have undefined slope. x=-5 is a vertical line. The slope of y = 7 is zero. The slope of x = y is one. The slope of x + y = 0 is negative one.

 10. A line passes through a point (2,5) and has a slope of -3.  What is the equation of a line perpendicular to this line through (2,5)? Choose: y = (1/3)x + 13/3 y = -3x + 17 y = -3x + 11 y = (1/3)x - 2/3 Explanation The perpendicular slope will be 1/3. y - 5 = (1/3) ( x - 2 ) y = (1/3)x + 13/3

 11. What is the slope of a line that would be perpendicular to the line shown in this graph? Choose: -1/2 2 1/2 -2 Explanation By counting, you can see that the slope of the shown line is 2 over 1 (RISE/RUN). The perpendicular will have a slope of -1/2.

 12. Which of these equations represents a line parallel to the line 2x + y = 6? Choose: y = 2x + 3 y - 2x = 4 2x - y = 8 y = -2x + 1 Explanation Lines that are parallel have the same slope. The slope of the given line is -2. Choice 4 is the only line whose slope is -2.  The others all have slopes equal to 2.

13.
 Find the slope of each side of the triangle A(1,1), B(5,2), C(3,4) and the slopes of the altitudes to each side.

14.
 A rancher is putting up a new fenced in area for his horses.  The corners of the fenced area are located at A(0,0), B(20,0), C(8,24) and D(-8,16).  a. By checking slopes, show the relationship between and  .  b.  By checking slopes, show the relationship between , and . c.  What kind of quadrilateral is the pasture, and why?

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