Step-by-step explanation:
simplify the three equations to get the common (Y) and we get the following:
1. [tex]Y = \frac{-5}{2}x + \frac{1}{2}\\[/tex]
2. [tex]Y = \frac{2}{5}x - 8[/tex]
3. [tex]Y = \frac{2}{5}x + \frac{4}{5}[/tex]
Line 1 and 2 are perpendicular because for the gradient(m) the fraction in line 1 for x is the negative reciprocal to line 2.
Line 1 and 3 are also perpendicular because for the gradient(m) the negative reciprocal can also be seen
*note for perpendicular lines the +c or y-intercept is neglected as it does not affect the perpendicularity
Line 2 and Line 3 are parallel because they have the same gradient of [tex]\frac{2}{5}x[/tex]
So they will have the same slope, regardless of the y-intercept.
