Question

Find equation of line parallel to 2x+5y=8 at point (-1,0)

Answer 1

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:

$5y=-2x+8$ so

$y=-\frac{2}{5}x+\frac{8}{5}$.

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:

$0=-\frac{2}{5}(-1)+b$ so

$0=\frac{2}{5}+b$ and

$b=-\frac{2}{5}$.

Now that we have the slope and the y-intercept (the b value we just solved for), we can write the new equation:

$y=-\frac{2}{5}x-\frac{2}{5}$.

There you go!