Respuesta :

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

[tex]y=mx+b[/tex]

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

[tex]\begin{cases}m=-3 \\ b=0\end{cases}[/tex]

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

[tex]y=-3x+b[/tex]

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

[tex]-5=-3\cdot1+b\Rightarrow-5=-3+b\Rightarrow b=-2[/tex]

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

[tex]y=-3x-2[/tex]