Question

Need help please!! Fast!!

Answer 1

Perpendicular

Explanation:

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

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Recall the slope-intercept form of a line:

`\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 identical slopes, they run parallel to each other.
• When the slopes of the lines are negative reciprocals of one another, the lines are perpendicular.
• In cases where the slopes are neither equal nor negative reciprocals, the lines do not fit into the classifications of being parallel or perpendicular.

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Our given lines:

y = 6x - 3

y = (-1/6)x + 7

Let's analyze the given lines:

The slopes of the lines can be determined by looking at the coefficients of the x terms.

For Line 1, the coefficient of the x term is 6, so its slope is 6.

For Line 2, the coefficient of the x term is -1/6, so its slope is -1/6.

These slopes are negative reciprocals of each other, thus these lines are perpendicular.

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Additional Information:

Reciprocal: The reciprocal of a number is found by dividing 1 by that particular number. For any non-zero value 'a', its reciprocal 'b' is given by:

• b = 1 / a

Negative Reciprocal: To derive the negative reciprocal of a number, first calculate its reciprocal, and then reverse the sign to make it negative. For a non-zero number 'a', the negative reciprocal 'c' is defined as:

• c = -1 / a