Mechanical Engineering Review Online

1. Find the equation of line with slope of -7 and x-intercept of 5.

a. 8x + y - 35 = 0

b. 7x + 3y – 30 = 0

c. 7x – y – 35 = 0

d. 8x + y + 35 = 0

2. Find the slope-intercept equation of a line that has y-intercept -5 and is parallel to the line of 6x – 3y = 4.

a. y = 3x + 6

b. y = 2x – 7

c. y = 2x – 5

d. y = 3x - 1

3. Find the equation of the locus of a point that moves so as to be always equidistant from A (4, 5) and B (-1, 2).

a. 6x – 4y – 20 = 0

b. 7x + 3y + 22 = 0

c. 5x + 3y – 18 = 0

d. 5x – 3y + 18 = 0

4. Find the distance between two parallel lines 5x – 4y + 11 = 0 and 5x - 4y + 3 = 0.

a. 1.24

b. 2.22

c. 1.88

d. 1.61

5. Find the distance between 4x + 5y = 6 and point (1, 5).

a. 2.81

b. 3.59

c. 2.00

d. 3.28

6. Which of the following lines is perpendicular to a line with the equation y = ½x + 8?

a. 3x + y – 9 = 0

b. 2x – 3y – 10 = 0

c. 2x + y – 8 = 0

d. 3x – 2y + 6 = 0

7. Find the y-intercept of line whose equation is 4x + 5y = 15.

a. 2

b. 3

c. 4

d. 5

8. The equation of a straight line passing through point (3, 4) and slope of 2.

a. x – y = -1

b. x + y = 1

c. x + 2y = -1

d. 2x + y = 1

9. The intercept of a straight line on the x-axis is -4. If (6, 3) is a point on the straight line, the slope of the straight line is ____.

a. 7/6

b. 6/7

c. -3/5

d. -6/7

10. The acute angle between the two straight lines y = 3x + 3 and y = 4x + 8, is ____.

a. 5.3 deg

b. 6.2 deg

c. 4.1 deg

d. 4.4 deg

11. Find the equation of line whose x-intercept is 3 and y-intercept is 4.

a. 2x + 5y = 10

b. x + 3y = -8

c. 2x – 4y = 12

d. 3x + 4y = 12

12. Find the slope of line whose equation is y – 6x + 3 = 0.

a. 3

b. 4

c. 5

d. 6

13. What is the equation of the straight line whose nearest point to the origin is (-7, 5)?

a. 3x – 8y = 20

b. 2x + 7y = 18

c. 5x – 6y = 22

d. 2x + 7y = 21

14. Find the equation of the line passing through the point (3, 2) and that is perpendicular to the line passing through (4, -3) and (-7, 6).

a. 7y = 6x + 11

b. 6y = 5x – 12

c. 8y = 9x – 11

d. 5y = 10x + 9

15. Find the slope form of the line passing through the points (-7, -4.3) and (6.3, -8.1).

a. y = 2/5x + 60/11

b. y = 2/7x + 63/10

c. y = 3/7x + 60/10

d. y = 5/7x + 63/10

16. Find the slope form of the line passing through the points (2, 3) and (9, 10).

a. y = x – 1

b. –y = x + 1

c. y = x + 1

d. y = -x + 1

17. What is the angle between the x-axis and the line y=0.9x?

a. 32 deg

b. 40 deg

c. 44 deg

d. 42 deg

18. Find the distance between point (0, 6) and (7, -2).

a. 9.3

b. 12.8

c. 10.6

d. 8.1

19. Find the mid-point between (3, 6) and (-5, -6).

a. (-1, 0)

b. (1, 1)

c. (1, 0)

d. (-1, -1)

20. Find the distance between two parallel lines 3x – 5y = 11 and 3x – 5y = 3.

a. 1.4

b. 1.8

c. 1.2

d. 2.1

21. The equation of the line through (1, 3) parallel to the line 4x – 3y + 5 = 0 is ____.

a. 3x – 4y + 5 = 0

b. 4x + 3y – 5 = 0

c. 3x + 5x + 6 = 0

d. 4x – 3y + 5 = 0

22. Find the equation of line whose x-intercept is 3 and y-intercept is 8.

a. 7x – 3y = 20

b. 8x – 5y = 22

c. 7x + 6y = 23

d. 8x + 3y = 24

23. Find the equation of the line whose y-intercept is -9 and whose slope is 5/4.

a. 6x – 5y – 35 = 0

b. 5x – 8y + 30 = 0

c. 5x – 4y – 36 = 0

d. 6x – 5y + 30 = 0

24. Find the slope of a line having a parametric equation of x = 3 + t and y = 6 – 4t.

a. 4

b. 5

c. -4

d. -5

25. Determine A such that 4x + 3y – 8 = 0 is perpendicular to 3x – Ay + 3 = 0.

a. 3

b. 4

c. 5

d. 6

26. A line passes thru (2, -4) and (-5, 3). Write the equation of the line in slope intercept form.

a. y = x + 2

b. y = -x – 2

c. 2y = x + 3

d. –y = x - 2

27. In a Cartesian coordinates, the vertices of a triangle are defined by the following points: (-3, 1), (5, 0) and (4, 4). Find the area?

a. 15.5

b. 16.3

c. 18.2

d. 14.5

28. Determine the coordinates of the point which is three-fifths of the way from the point (3, -6) to the point (-4, 6)

a. (-6/5, 6/5)

b. (6/5, -6/5)

c. (5/6, -5/6)

d. (-5/6, 6/5)

Answer Key (Handouts)