Question

1.A line is parallel to the line 5x+y+4=0 Work out it's gradient (The answer is a whole number or decimal.)

Answer 1

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.