Question

Find the equation of a line that is parallel to the line and contains the point

Answer 1

Lines can be written in slope-intercept form, and this form is:

`y=mx+b`

Where 'm' represents the slope of the line, and 'b' represents the y-intercept. The line given in the question is written in this form, with the following coefficients

`\begin{cases}m=-3 \\ b=0\end{cases}`

Parallel lines, have the same slope. It means, our parallel line have the following form

`y=-3x+b`

Now, we can just use our given point to find out the 'b' coefficient. Our point is (1, -5), making the substitution, we have

`-5=-3\cdot1+b\Rightarrow-5=-3+b\Rightarrow b=-2`

Our parallel line that contains the point (1, -5) is

`y=-3x-2`