Answered

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

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

Sagot :

GinnyAnswer
To find the slope of a line given by an equation in the slope-intercept form, we first need to understand the structure of this form. The slope-intercept form of a linear equation is:

[tex]\[ y = mx + b \][/tex]

where:
- [tex]\( m \)[/tex] represents the slope of the line.
- [tex]\( b \)[/tex] represents the y-intercept of the line.

Given the equation:

[tex]\[ y = \frac{2}{3} - 5x \][/tex]

we need to rewrite it in the slope-intercept form. Notice this equation is already in a form where the slope can be identified directly:

[tex]\[ y = -5x + \frac{2}{3} \][/tex]

Now, comparing it with the form [tex]\( y = mx + b \)[/tex]:

- The coefficient of [tex]\( x \)[/tex] is [tex]\( -5 \)[/tex].
- So, [tex]\( m = -5 \)[/tex].

Thus, the slope of the line represented by the equation [tex]\( y = \frac{2}{3} - 5x \)[/tex] is:

[tex]\[ -5 \][/tex]

Therefore, the correct answer is:
[tex]\[ -5 \][/tex]
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