$\"\"$

\

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

\

and b is the y-intercept.

\

Write the equation 1 in slope-intercept form

\

3y = 2x + 14

\

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

\

$\"\"$ (Cancel common terms)

\

$\"\"$ ………………….(1)

\

$\"\"$

\

Write the equation 2 in slope-intercept form.

\

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

\

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

\

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

\

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

\

$\"\"$ (Cancel common terms)

\

$\"\"$ (Multiply each side by negative one) \ \

\

$\"\"$ (Product of two same signs is positive) \ \

\

$\"\"$ …………………..(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.