Question

Which is the ordered pair for the point on the x-axis that is on the line parallel to the given line and through the given point (–6, 10)?

(6, 0)
(0, 6)
(−5, 0)
(0, −5)

Answer 1

slope of given line = -10/12= -5/6
eqof line parallel to it =
y -10= -5/6 ( x+6)

put y =0

-10 = -5/6. (x+6)
x=6

so( 6,0)

Answer 2

The equation of line shown in the graph which passes through (-8,6) and (4,-4) is given by,

→  $\frac{y-6}{x+8}=\frac{6+4}{-8-4}$

→$\frac{y-6}{x+8}=\frac{-5}{6}$

Slope of line = -5/6

→6 × (y-6) = -5(x+8)

→ 6 y -36= -5 x -40

→ 5 x + 6 y +4=0

→ 6 y =-5 x -4

→ y = -5 x/6 - 4/6

Slope of line = -5/6

Equation of line parallel to→ 5 x + 6 y+4=0 is given by→ 5 x + 6 y+k=0

As given the line  5 x + 6 y+k=0,  passes through (-6,10).

→5×(-6) + 6×10 +k=0

→ -30 +60+k=0

k= -30

The line is→ 5 x + 6 y -30 =0

Out of four options given , (6,0) satisfies 5 x + 6 y -30 =0 i.e 5×6 +6×0-30=30 - 30=0=R.H.S

Hence option A (6,0) is the ordered pair for the point on the x-axis that is on the line→ 5x+6y-30=0 parallel to the given line→ 5 x+6y+4=0 and through the given point (–6, 10)?