The line through (2, -1) and parallel to a line wit slope of 3/4?

Question

1. Indicate the equation of the given line in standard form. 

The line through (2, -1) and parallel to a line with slope of 

2. D(5, -2) m = 2/5 

3.The line with slope 9/7 and containing the midpoint of the segment whose endpoints are (2, -3) and (-6, 5). 

4.The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2). 
Any help would be much appreciated!

 

 

Answer 1

(2).

• The standard form line equation is Ax + By = C. A shouldn't be negative, A and B shouldn't both be zero, and A, B and C should be integers.

• The point-slope form of line equation : y - y₁ = m (x - x₁), where (x₁, y₁) is point and m is slope.

Let the point (x₁, y₁) = (5, - 2) and slope m = 2/5.

The point-slope form of line equation : y - y₁ = m (x - x₁).

y - (- 2) = (2/5) [ x - (5) ]

Multiply each side by 5.

5(y + 2) = 2(x - 5)

Apply distributive property : a(b + c) = ab + ac.

5(y) + 5(2) = 2(x) + 2(- 5)

5y + 10 = 2x - 10

Subtract 5y from each side.

5y + 10 - 5y = 2x - 10 - 5y

10 = 2x - 10 - 5y

Add 10 to each side.

10 + 10 = 2x - 10 - 5y + 10

20 = 2x - 5y

The standard form of line equation is 2x - 5y = 20.

 

Answer 2

(1).

• The standard form line equation is Ax + By = C. A shouldn't be negative, A and B shouldn't both be zero, and A, B and C should be integers.
• If two nonvertical lines in the same plane are parallel, then they have the same slope.
• The point-slope form of line equation : y - y₁ = m (x - x₁), where (x₁, y₁) is point and m is slope.

Let the point (x₁, y₁) = (2, - 1) and slope m = 3/4.

The point-slope form of line equation : y - y₁ = m (x - x₁).

y - (- 1) = (3/4) [ x - (2) ]

Multiply each side by 4.

4(y + 1) = 3(x - 2)

Apply distributive property : a(b + c) = ab + ac.

4(y) + 4(1) = 3(x) + 3(- 2)

4y + 4 = 3x - 6

Subtract 4y from each side.

4y + 4 - 4y = 3x - 6 - 4y

4 = 3x - 6 - 4y

Add 6 to each side.

4 + 6 = 3x - 6 - 4y + 6

10 = 3x - 4y

The standard form of line equation is 3x - 4y =10.

 

Answer 3

(3).

• The standard form line equation is Ax + By = C. A shouldn't be negative, A and B shouldn't both be zero, and A, B and C should be integers.

• The point-slope form of line equation : y - y₁ = m (x - x₁), where (x₁, y₁) is point and m is slope.
• The midpoint formula: [ (x₁ + x₂)/2, (y₁ + y₂)/2 ], where (x₁, y₁) and (x₂, y₂) are end points of the segment.

Let the points are A = (x₁, y₁) = (2, - 3) and B = (x₂, y₂) = (- 6, 5).

Midpoint between A and B : [ (x₁ + x₂)/2, (y₁ + y₂)/2 ]

= [ {(2) + (- 6)}/2, {(- 3) + (5)}/2 ]

= [ - 4/2, 2/2 ]

= [ - 2, 1 ]

Let the point are (x₁, y₁) = (- 2, 1) and slope m = 9/7.

The point-slope form of line equation : y - y₁ = m (x - x₁).

y - (1) = (9/7) [ x - (- 2) ]

Multiply each side by 7.

7(y - 1) = 9(x + 2)

Apply distributive property : a(b + c) = ab + ac.

7(y) + 7(- 1) = 9(x) + 9(2)

7y - 7 = 9x + 18

Subtract 7y from each side.

7y - 7 - 7y = 9x + 18 - 7y

- 7 = 9x + 18 - 7y

Subtract 18 from each side.

- 7 - 18 = 9x + 18 - 7y - 18

- 25 = 9x - 7y

The standard form of line equation is 9x - 7y = - 25.

 

Answer 4

(4).

• The midpoint formula: [ (x₁ + x₂)/2, (y₁ + y₂)/2 ], where (x₁, y₁) and (x₂, y₂) are end points of the segment.
• The slope m : [ (y₂ - y₁) / (x₂ - x₁) ], where (x₁, y₁) and (x₂, y₂) are points.
• If two nonvertical lines in the same plane are perpendicular, then their slopes are negative reciprocals.
• The point-slope form of line equation : y - y₁ = m (x - x₁), where (x₁, y₁) is point and m is slope.
• The standard form line equation is Ax + By = C. A shouldn't be negative, A and B shouldn't both be zero, and A, B and C should be integers.

Let the points are A = (x₁, y₁) = (1, 0) and B = (x₂, y₂) = (5, - 2).

Midpoint between A and B : [ (x₁ + x₂)/2, (y₁ + y₂)/2 ]

= [ {(1) + (5)}/2, {(0) + (- 2)}/2 ]

= [ 6/2, - 2/2 ]

= [ 3, - 1 ]

The slope of AB line m = [ (y₂ - y₁) / (x₂ - x₁) ] = [(- 2) - (0)] / [(5) - (1)] = - 2/4 = - 1/2.

Let the point are (x₁, y₁) = (3, - 1) and slope m = 2.

The point-slope form of line equation : y - y₁ = m (x - x₁).

y - (- 1) = 2[ x - (3) ]

y + 1 = 2(x - 3)

Apply distributive property : a(b - c) = ab - ac.

y + 1 = 2x - 6

Subtract y from each side.

y + 1 - y = 2x - 6 - y

1 = 2x - 6 - y

Add 6 to each side.

1 + 6 = 2x - 6 - y + 6

7 = 2x - y

The standard form of line equation is 2x - y = 7.