equation of the line

Question

1) write an equation of the line parallel  to x+2y=6 through (8,3)

2) find the equation of a line containing points (-2,8) and (3,5)

3) write an equation of the line parallel  to y=3x-2 through (1,-3)

Answer 1

1)write an equation of the line parallel  to x+2y=6 through (8,3)

Given equation is x+2y=6

The parallel  equation is x+2y=k---------Equation(1)

Equation(1) passes through point (8,3)

substitute the values x=8,y=3 in Equation(1)

8+2(3)=k

8+6=k                                         (Multiply: 2×3=6)

14=k                                           (Add: 8+6=14)

substitute k value in Equation(1)

The required equation is x+2y=14.

2)write an equation of the line containing points (-2, 8) and (3, 5).

Given points (-2, 8) and (3, 5).

The general slope formula m = (y2 - y1)/( x2 - x1)

substitute the values x1= -2,y1= 8 and x2 = 3, y2 = 5

m = (5 - 8)/( 3 - (-2))

Product of two same sings is positive.

m = (5 - 8)/( 3 + 2)

m = -3/5

The slope - intercept form of a line equation is (y - y1) = m (x - x1)

substitute the values x1= -2,y1= 8 and m = -3/5

(y - 8) = -3/5 (x - (-2))

(y - 8) = -3/5 (x +2)

5(y - 8) = -3(x +2)

5y - 40 = -3x -6

3x + 5y -34 = 0

3)write an equation of the line parallel  to y=3x-2 through (1,-3)

Given equation is y=3x-2

y = 3x - 2                           (Subtract y from each side)

y - y = 3x - 2 - y

y - y = 3x - y - 2                 (Commutative property: a+b=b+a)

0 = 3x - y - 2                      (Additive inverse property: y - y = 0)

0+2 = 3x-y-2+2                  (Add 2 to each side)

0+2 = 3x-y-2+2                  (Additive indentity property: 0 +2 = 2)

2 = 3x-y-2+2

2 = 3x-y+0                        (Additive inverse property: -2 + 2 = 0)

2 = 3x-y                            (Additive indentity property: 3x+y + 0 = 3x+y)

3x-y = 2

the parallel line equation is  3x - y = k --------> (1)

(1) is passes through the point (1,-3)

                3(1)-(-3)=k         (Product of two same signs is positive)

                3+3=k               (Add:3+3 = 6)

                k = 6

Substitute k =6 in equation 3x - y = k.

                                       3x - y = 6.