A linear equation in the standard (x, y) coordinate plane is given by y = -4. Is the state… — ACT

A linear equation in the standard $(x, y)$ coordinate plane is given by $y = -4$ . Is the statement that the slope of this line is undefined true or false?

Cevap: Cevap

Cevap

False

The correct answer is false because the line

y = -4

is horizontal, and all horizontal lines have a slope of

0

. A slope is only undefined for vertical lines, which are written in the form

x = c

Adım Adım Çözüm

Identify the orientation of the line given by the equation

y = -4

The equation is of the form

y = c

, where

c

is a constant. This represents a horizontal line where every point on the line has a

y

-coordinate of

-4

Since the

y

-value never changes regardless of the

x

-value, the line is parallel to the

x

-axis.

Calculate the slope using two points on the line.

Let the two points be

(0, -4)

and

(1, -4)

. The slope

m

is given by

m = \frac{-4 - (-4)}{1 - 0} = \frac{0}{1} = 0

The slope formula is

m = \frac{y_2 - y_1}{x_2 - x_1}

Compare the calculated slope to the statement in the question.

The calculated slope is

0

, which is a defined number. The statement claims the slope is undefined, which is only true for vertical lines. Therefore, the statement is false.

An undefined slope occurs when dividing by zero, which is not the case for a horizontal line.

Anahtar Kavram

The slope of any horizontal line is

0

, whereas the slope of any vertical line is undefined.

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