Question

Need help asap here is screenshot

Answer 1

Neither parallel nor perpendicular

Explanation:

To determine whether the given lines are parallel, perpendicular, or neither, we need to examine their slopes.

`\hrulefill`

The slope-intercept form of a linear equation is given as follows:

`\boxed{\left\begin{array}{ccc}\text{\underline{Slope-Intercept Form:}}\\\\y=mx+b\end{array}\right }`

Where 'm' represents the slope of the line.

• If two lines have the same slope, they are parallel.

• If the slopes are negative reciprocals of each other, the lines are perpendicular.
• If the slopes are neither equal nor negative reciprocals, then the lines are neither parallel nor perpendicular.

`\hrulefill`

Our given set of equations:

3x + 2y = 5

3y + 2x = -3

Let's rearrange the given equations into the slope-intercept form:

(1) 3x + 2y = 5

To get it into slope-intercept form, we solve for 'y':

⇒2y = -3x + 5

∴ y = (-3/2)x + 5/2

(2) 3y + 2x = -3

Solving for 'y':

⇒3y = -2x - 3

∴y = (-2/3)x - 1

Now that we have the equations in slope-intercept form, we can see the slopes more clearly:

The slope of the first line is -3/2.

The slope of the second line is -2/3.

Since these slopes are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular.

`\hrulefill`

Additional Information:

Reciprocal: The reciprocal of a number is simply 1 divided by that number. Mathematically, for a non-zero number 'a', its reciprocal 'b' is given by:

• b = 1 / a

Negative Reciprocal: When you take the reciprocal of a number and then negate (or make it negative), you get the negative reciprocal. So, if 'a' is a non-zero number, its negative reciprocal 'c' is given by:

• c = -1 / a