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What is the slope of the line represented by the equation [tex]y = -\frac{1}{2} x + \frac{1}{4}[/tex]?

A. [tex]-\frac{1}{2}[/tex]
B. [tex]-\frac{1}{4}[/tex]
C. [tex]\frac{1}{4}[/tex]
D. [tex]\frac{1}{2}[/tex]


Sagot :

To find the slope of the line represented by the equation [tex]\( y = -\frac{1}{2} x + \frac{1}{4} \)[/tex], let's break down the equation and understand its form.

The equation given is in the slope-intercept form of a linear equation, which is generally written as:
[tex]\[ y = mx + b \][/tex]

Here:
- [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the y-intercept of the line, which is the point where the line crosses the y-axis.

In the provided equation:
[tex]\[ y = -\frac{1}{2} x + \frac{1}{4} \][/tex]

we can identify the coefficient of [tex]\( x \)[/tex] to determine the slope. The coefficient of [tex]\( x \)[/tex] is [tex]\( -\frac{1}{2} \)[/tex].

Thus, the slope [tex]\( m \)[/tex] of the line is:
[tex]\[ m = -\frac{1}{2} \][/tex]

So, the correct answer is:
[tex]\[ -\frac{1}{2} \][/tex]

Therefore, the slope of the line represented by the equation [tex]\( y = -\frac{1}{2} x + \frac{1}{4} \)[/tex] is [tex]\( -\frac{1}{2} \)[/tex].

So, the correct choice is:
[tex]\[ -\frac{1}{2} \][/tex]