Question

Which lines are parellele

Answer 1

Line 1 and Line 4 are parallel lines

Solution:

General equation of a line:

y = mx + c

where m is the slope and c is the y-intercept of the line.

To find the slope of each line:

Line 1: $y=-\frac{3}{4} x-6$

Slope $(m_1)=-\frac{3}{4}$

Line 2: $y-7=-4(x+9)$

$y-7=-4x-36$

Add 7 on both sides, we get

$y=-4x-29$

Slope $(m_2)=-4$

Line 3: $y=-2 x+6$

Slope $(m_3)=-2$

Line 4: $x+\frac{4}{3} y=-5$

Subtract x from both sides, we get

$\frac{4}{3} y=-x-5$

Multiply  by $\frac{3}{4}$ on both sides, we get

$y=-\frac{3}{4}x-\frac{15}{4}$

Slope $(m_4)=-\frac{3}{4}$

Two lines are parallel, if their slopes are equal.

From the above slopes,

$m_1=m_4$

Therefore Line 1 and Line 4 are parallel lines.