If we arrange the equation of a line in standard form,
we can read its slope (gradient) directly.
1). 5x + y + 4 = 0
Subtract 4 from each side: 5x + y = -4
Subtract 5x from each side: y = -5x - 4
The slope (gradient) of the line is -5 .
2). Parallel lines have the same slope (gradient).
First, find the slope (gradient) of the given line.
3x + 5y = 15
Subtract 3x from each side: 5y = -3 x + 15
Divide each side by 5 : y = -3/5 x + 15
The slope (gradient) of the given line is -3/5 .
Any line with a slope (gradient) of -3/5 is parallel to this one.
Its equation will be y = -3/5 x + any number.