Answer:
(a) Neither
(a) Perpemdicular
Step-by-step explanation:
Required
Determine the relationship between given lines
(a)
[tex]y = -\frac{2}{5}x + 3[/tex]
and
[tex]y = \frac{2}{5}x + 7[/tex]
An equation written in form: [tex]y=mx + b[/tex] has the slope:
[tex]m \to slope[/tex]
So, in both equations:
[tex]m_1 = -\frac{2}{5}[/tex]
[tex]m_2 = \frac{2}{5}[/tex]
For both lines to be parallel
[tex]m_1 = m_2[/tex]
This is false in this case, because:
[tex]-\frac{2}{5} \ne \frac{2}{5}[/tex]
For both lines to be perpendicular
[tex]m_1 * m_2 = -1[/tex]
This is false in this case, because:
[tex]-\frac{2}{5} * \frac{2}{5} \ne -1[/tex]
(b)
[tex]5y + 2x = -10[/tex]
and
[tex]-5x + 2y = 4[/tex]
Write equations in form: [tex]y=mx + b[/tex]
[tex]5y + 2x = -10[/tex]
[tex]5y = -2x +10[/tex]
Divide by 5
[tex]y = -\frac{2}{5}x +2[/tex]
[tex]-5x + 2y = 4[/tex]
[tex]2y = 5x + 4[/tex]
Divide by 2
[tex]y = \frac{5}{2}x + 2[/tex]
In both equations:
[tex]m_1 = -\frac{2}{5}[/tex]
[tex]m_2 = \frac{5}{2}[/tex]
For both lines to be parallel
[tex]m_1 = m_2[/tex]
This is false in this case, because:
[tex]-\frac{2}{5} \ne \frac{5}{2}[/tex]
For both lines to be perpendicular
[tex]m_1 * m_2 = -1[/tex]
This is true in this case, because:
[tex]-\frac{2}{5} * \frac{5}{2} = -1[/tex]
Cancel out 2 and 5
[tex]-1 = -1[/tex]
