Question

A line is parallel to the equation 3y-x=-12 and this line also passes through the point (18,2). What is the equation of this line?

Answer 1

Given;

`3y-x=-12`

Recall that the equation of a straight line is given as;

`\begin{gathered} y=mx+c\text{ } \\ \text{Where m= slope of the line} \\ 3y=x-12 \\ y=(1)/(3)x-4 \\ \text{Thus, m=}(1)/(3) \end{gathered}`

The slope of two parallel lines is equal.

Thus, the slope of the second line is also 1/3;

Then, the equation is;

`\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where x}_1=18_{} \\ \text{and y}_1=2 \\ y-2=(1)/(3)(x-18) \\ 3(y-2)=x-18 \\ 3y-6=x-18 \\ 3y-x=6-18 \\ 3y-x=-12 \end{gathered}`

The equation of the line is also 3y - x = -12