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What is the slope of the line represented by the equation [tex]y=\frac{2}{3}-5x[/tex]?

A. [tex]\(-5\)[/tex]
B. [tex]\(\frac{2}{3}\)[/tex]
C. [tex]\(\frac{2}{3}\)[/tex]
D. [tex]\(5\)[/tex]


Sagot :

To determine the slope of the line represented by the equation [tex]\( y = \frac{2}{3} - 5x \)[/tex], let's analyze the equation in its standard slope-intercept form.

The standard form of a linear equation is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.

Given the equation:
[tex]\[ y = \frac{2}{3} - 5x \][/tex]

We can rewrite this equation in a form that more clearly resembles the slope-intercept form. Note that the order of terms doesn't affect the slope or intercept:
[tex]\[ y = -5x + \frac{2}{3} \][/tex]

Here, the equation is in the form [tex]\( y = mx + b \)[/tex]:
- [tex]\( m \)[/tex] is the coefficient of [tex]\( x \)[/tex], which is [tex]\(-5\)[/tex].
- [tex]\( b \)[/tex] is the constant term, which is [tex]\(\frac{2}{3}\)[/tex].

Therefore, the slope [tex]\( m \)[/tex] of the line is [tex]\(-5\)[/tex].

Among the given choices:
- [tex]\( -5 \)[/tex]
- [tex]\( \frac{2}{3} \)[/tex]
- [tex]\( \frac{2}{3} \)[/tex]
- [tex]\( 5 \)[/tex]

The correct answer is:
[tex]\[ -5 \][/tex]
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