Need some help solvin these math problems.

Question

10) Solve the following inequality. Write the solution set using interval notation and graph the solution set on a number line: 3x-1>8 or 3x-4<-1

 

4) Determine whether each pair of lines are parallel, perpendicular, or neither. Also, state the reason how.

a. y=-5x+1 and x-5y=10






b. 2x+3y=21 and 6y=-4x-24) Determine whether each pair of lines are parallel, perpendicular, or neither. Also, state the reason how.

a. y=-5x+1 and x-5y=10






b. 2x+3y=21 and 6y=-4x-2

 

 

1) Sketch graph of 2x+3y=12 by plotting ordered pair solutions.

Answer 1

3x-1>8 or 3x-4<-1

 

Note that the "or" means the area is included if it satisfies either condition.

It does not necessarily have to satisfy both conditions.

 

3x - 1 > 8    3x - 4 < -1

3x > 9         3x < 3

x > 3           x < 1

 

All numbers that are greater than 3 work as well as all numbers less than 1.

 

(-∞,1) U (3, ∞)

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a. y=-5x+1 and x-5y=10

 

Slope intercept form is y = mx + b where m = slope, b = y-intercept.

Parallel lines have the same slope and different y-intercepts.

Perpendicular lines have slopes that are negative reciprocal ...m_p = -1/m

Any other case, the lines are neither parallel or perpendicular

 

y = -5x + 1

m = -5

 

x - 5y = 10

5y = x - 10

y = (1/5)x - 2

m = 1/5

 

Slope 1 is -5

Slope 2 is 1/5 ... 1/5 = -1/(-5)

so m₂ = -1/m  

Lines are PERPENDICULAR

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b. 2x+3y=21 and 6y=-4x-2

 

Solve both equations for y or use the fact that:

For standard form linear equations ax² + bx = c

the slope is:  m = -a/b

 

2x + 3y = 21

m = -2/3

 

6y = -4x -2

m = -4/6 = -2/3

 

Slopes are the same so the lines are PARALLEL

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2x+3y=12

3y = -2x + 12

y = (-2/3)x + 4

 

Just plug in values for x and find the corresponding value of y from (-2/3)x+4.

Simplest thing is to use multiples of 3 and the y-intercept which is (0, 4)

 

x         (-2/3)x+4

----------------------

-3           6

 0           4

 3           2

 

Plot the points and draw the line