To find the equation of a line when having the slope and a point, we use the point-slope equation:
[tex]y-y_1=m(x-x_1)[/tex]Where m is the slope and (x1,y1) is the point.
In this case, since the point is (0,0):
[tex]\begin{gathered} x_1=0 \\ y_1=0 \end{gathered}[/tex]And we are told that the line is parallel to a line that has a slope of -6. Something that is important to solve this problem is:
• Parallel line have ,the same slope
So the slope of the line is also -6:
[tex]m=-6[/tex]Now we are ready to use the point-slope equation:
[tex]y-y_1=m(x-x_1)[/tex]Substituting m, x1, and y1:
[tex]y-0=-6(x-0)[/tex]Simplifying the expression, we get the slope-intercept form:
[tex]y=-6x[/tex]Answer: y=-6x
