Question

the equation od three lines are given below

Answer 1

Two lines are parallel if they have the same slope and the are perpendicular if m_2 = -1/m_1.

We first write the three lines in slope-intercept form:

Line 1:

$6x+4y=4$

subtracting 6x from both sides gives

$4y=4-6x$

Dividing both sides by 4 gives

$y=\frac{4-6x}{4}$$y=-\frac{3}{2}x+1$

Line 2:

Dividing both sides by 3 gives

$y=-\frac{2}{3}x+\frac{7}{3}$

Line 3:

This equation is already in slope-intercept form:

$y-\frac{2}{3}x-5$