Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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 find the slope of the line represented by the equation [tex]\( y = -\frac{2}{3} - 5x \)[/tex], we need to identify the slope-intercept form of a linear equation, which is:

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

Here, [tex]\( m \)[/tex] represents the slope of the line, and [tex]\( b \)[/tex] is the y-intercept. In this form, the coefficient of [tex]\( x \)[/tex] is the slope.

The given equation is:

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

We can rewrite the equation to fit the slope-intercept form [tex]\( y = mx + b \)[/tex]:

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

Now, we compare it to the standard form [tex]\( y = mx + b \)[/tex]:

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

From this comparison, we can see that:
- The coefficient of [tex]\( x \)[/tex] is [tex]\(-5\)[/tex], which means the slope, [tex]\( m \)[/tex], is [tex]\(-5\)[/tex].

Therefore, the slope of the line is:

[tex]\[ \boxed{-5} \][/tex]