$\"\"$

The line equation in slope-intercept form is $\"\"$ , where m is the slope and b is the y-intercept.

Write the equation 2 in slope-intercept form.

$\"\"$ (Subtract 2x from each side)

$\"\"$ (Apply additive inverse property: $\"\"$ )

$\"\"$ (Divide each side by negative 3 )

$\"\"$ (Cancel common terms) \ \

$\"\"$ …………………..(1)

Write the equation 1 in slope-intercept form

3y = 2x + 14

$\"\"$ (Divide each side by negative 3 )

$\"\"$ (Cancel common terms)

$\"\"$ ………………….(2) $\"\"$

Next find the slope of the equations.

Slope of the first equation is $\"\"$

Slope of the second equation is $\"\"$ $\"\"$

If two lines are parallel, their slopes must be equal.

Slopes of the lines are equal. So, the lines are parallel. $\"\"$

The lines are parallel.