Question

Could somebody help n explain pls thx

Answer 1

Answer:

lines are perpendicular

Step-by-step explanation:

• Parallel lines have equal slopes

• The product of the slopes of perpendicular lines = - 1

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange the given equations into this form and extract the slope

3x - 2y = - 6 ( subtract 3x from both sides )

- 2y = - 3x - 6 ( divide through by - 2 )

y = $\frac{3}{2}$ x + 3 ← in slope- intercept form

with slope m = $\frac{3}{2}$

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4x + 6y = 2 ( subtract 4x from both sides )

6y = - 4x + 2 ( divide through by 6 )

y = - $\frac{4}{6}$ x + $\frac{2}{6}$ , that is

y = - $\frac{2}{3}$ x + $\frac{1}{3}$ ← in slope- intercept form

with slope m = - $\frac{2}{3}$

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$\frac{3}{2}$ ≠ - $\frac{2}{3}$ , then lines are not parallel

$\frac{3}{2}$ × - $\frac{2}{3}$ = - 1

Thus the lines are perpendicular to each other