Write an equation of the line that passes through (6,−3) and is parallel to the line y=−2/3x+5.

Answer 1

First we will find the slope of the given line Y = -2/3X + 5 , that is equal to -2/3

general eqation of a line with slope m is y = mx + b

so m = -2/3

the general equation of a line passes through the point (x₁, y₁ ) is , y-y₁ = m ( x - x₁)

so we have points (6,-3) the line passes through and same slope is -2/3 , its same , because line is parellal to the given line .

we can write the equation of the required line is y-(-3) = -2/3 ( x- 6 )

y+ 3 = -2/3x + 2/3*6

y+ 3 = -2/3x + 4

subtracting 3 from both sides,

y = - 2/3x + 1.. Ans.