Math Help ASAP?

Question

1. Indicate in standard form the equation of the line passing through the given point and having the given slope.

R(4, 0), m = 5

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

The line that is the perpendicular bisector of the segment whose endpoints are R(-1, 6) and S(5, 5)

3.The line that contains the point Q( 1, -2) and is parallel to the line whose equation is

y - 4 = 2/3 (x - 3)

Answer 1

• 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.

Slope (m) = 5 and the point is R(4, 0).

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

Slope (m) = 5.

Now, the line equation is y = 5x + b.

Find the y - intercept by substituting the point in the line equation say R(x, y) = (4, 0).

0 = (5)(4) + b

b = 0 - 20

⇒ b = - 20.

The equation is y = 5x - 20.

Subtract y from each side.

0 = 5x - y - 20

Add 20 to each side.

5x - y = 20.

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

• 2).

End points of the segment are R(- 1, 6) and S(5, 5).

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

Let the points are R(x₁, y₁) = (- 1, 6) and S(x₂, y₂) = (5, 5).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m = [(5 - 6)/(5 - (- 1))]

m  = [- 1/(5 + 1)]

⇒ m = - 1/6.

Because the slopes of perpendicular lines are negative reciprocals, the slope of perpendicular is 6.

Now, the perpendecular line equation is y = 6x + b.

Find the y - intercept, we need a point on the perpendicular bisector, to find this point we will find the midpoint of R and S:

midpoint = [ (- 1 + 5)/2, (6 + 5)/2 ]
             = [ 4/2, 11/2 ]

             = [ 2, 5.5 ].

Find the y - intercept by substituting the midpoint in the perpendecular line equation say (x, y) = (2, 5.5).

5.5 = (6)(2) + b

b = 5.5 - 12

⇒ b = - 6.5.

The perpendecular line equation  is y = 6x - 6.5.

Subtract y from each side.

6x - y - 6.5 = 0

Add 6.5 to each side.

6x - y = 6.5.

The standard form the equation of the line is 6x - y = 6.5.

• 3).

The line equation is y - 4 = (2/3)(x - 3).

Write the equation in slope - intercept form.

y - 4 = (2/3)x - 2

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

y = (2/3)x + 2.

Comapare the equation with slope - intercept form.

Slope (m) = 2/3

Because the parallel lines have same slopes, the slope of parallel line through the point Q(1, - 2) is 2/3.

Now the parallel line equation is y = (2/3)x + b.

Find the y - intercept by substituting the point in the parallel line equation say Q(x, y) = (1, - 2).

- 2  = (2/3)(1) + b

b = - 2 - 2/3

b = (- 6 - 2)/3

⇒ b = - 8/3.

The parallel line equation is y = (2/3)x - (8/3).