Lines are parallel if they have the same slope. In order to write a new equation parallel to the one we are given, we have to know the slope of the line we are given. Solve it for y:
[tex] 5y=-2x+8 [/tex] so
[tex] y=-\frac{2}{5}x+\frac{8}{5} [/tex].
That means that the slope of the given line is -2/5. We will now use the point we were given and fill in the slope-intercept form of a line with the x coordinate of -1 and the y coordinate of 0:
[tex] 0=-\frac{2}{5}(-1)+b [/tex] so
[tex] 0=\frac{2}{5}+b [/tex] and
[tex] b=-\frac{2}{5} [/tex].
Now that we have the slope and the y-intercept (the b value we just solved for), we can write the new equation:
[tex] y=-\frac{2}{5}x-\frac{2}{5} [/tex].
There you go!
