equation of the line

Question

4) write an equation of the line perpendicular  to x+y=-3 through (0,4)

5) write an equation of the line parallel  to 2x-y=1 through (-1,2)

6)write an equation of the line parallel  to x-y=-4 through (1,-3)

Answer 1

5) write an equation of the line parallel  to 2x-y=1 through (-1,2)

Given equation is

2x-y=1

The parallel line equation is  2x - y = k --------> (1)

(1) is passes through the point (-1,2)

                2(-1)-(2)=k                         (Product of two same signs is positive)

                -2-2=k                          

                k = -4                         

Substitute k =-4 in equation 2x - y = k.

                                     2x - y = -4

6) write an equation of the line parallel  to x-y=-4 through (1,-3)

A) given equation x-y=-4

the parallel line equation is x-y=k-------(1)

the line is passing through (1,-3)

1-(-3)=k           (Substitute x=1 and y=-3)

1+3=k             (The product of two same signs is positive)

4=k                 (Add: 1+3=4)

k=4

substitute k=4 in equation (1)

x-y=4.

Answer 2

4).

The line equation is x + y = - 3.

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

Write the equation in slope - intercept form.

y = - x - 3.

Compare the equation with slope - intercept form.

Slope (m) = - 1.

Because the slopes of perpendicular lines are negative reciprocals, the slope of perpendicular is 1.

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

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

4 = (1)(0) + b

⇒ b = 4.

The perpendecular line equation  is y = x + 4.