To find the equation of a line that passes through a point and parallel to another line, we can use the point-slope form.
[tex]y-y_1=m(x-x_1)[/tex]
First, let's find out what the slope m should be. Remember that parallel lines have the same slope.
[tex]\begin{gathered} y=mx+b \\ y=-6x+1 \end{gathered}[/tex]
We see that the slope is -6.
Now that we have the slope, we just need to plug in the coordiantes of the point and the slope to the point-slope format of the equation. Then, we will rewrite it in point-intercept form.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-1)=-6(x-1) \\ y+1=-6(x-1) \\ y+1=-6x+6 \\ y=-6x+5 \end{gathered}[/tex]
The answer is y = -6x + 5.
