Answer :
Certainly! To find the slope and the y-intercept of the linear function [tex]\( p(x) = -4 - \frac{4}{3}x \)[/tex], we can analyze its form. A linear equation is typically written in the standard form:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
Now, let's rewrite the given function in this form:
[tex]\[ p(x) = -4 - \frac{4}{3}x \][/tex]
Comparing this with [tex]\( y = mx + b \)[/tex], we can identify the terms:
- The term [tex]\(-\frac{4}{3}x\)[/tex] corresponds to [tex]\( mx \)[/tex], indicating that the slope [tex]\( m \)[/tex] is [tex]\(-\frac{4}{3}\)[/tex].
- The term [tex]\(-4\)[/tex] corresponds to [tex]\( b \)[/tex], indicating that the y-intercept [tex]\( b \)[/tex] is [tex]\(-4\)[/tex].
Thus, the slope of the function [tex]\( p(x) \)[/tex] is [tex]\(-\frac{4}{3}\)[/tex] and the y-intercept is [tex]\(-4\)[/tex].
To express the y-intercept as an ordered pair, we consider the point where the line intersects the y-axis. This occurs when [tex]\( x = 0 \)[/tex]. Substituting [tex]\( x = 0 \)[/tex] into the equation gives us:
[tex]\[ y = -4 - \frac{4}{3}(0) = -4 \][/tex]
So the y-intercept as an ordered pair is:
[tex]\[ (0, -4) \][/tex]
In summary:
- The slope is [tex]\(-\frac{4}{3}\)[/tex].
- The y-intercept is [tex]\(-4\)[/tex].
- The y-intercept as an ordered pair is [tex]\((0, -4)\)[/tex].
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] represents the slope and [tex]\( b \)[/tex] represents the y-intercept.
Now, let's rewrite the given function in this form:
[tex]\[ p(x) = -4 - \frac{4}{3}x \][/tex]
Comparing this with [tex]\( y = mx + b \)[/tex], we can identify the terms:
- The term [tex]\(-\frac{4}{3}x\)[/tex] corresponds to [tex]\( mx \)[/tex], indicating that the slope [tex]\( m \)[/tex] is [tex]\(-\frac{4}{3}\)[/tex].
- The term [tex]\(-4\)[/tex] corresponds to [tex]\( b \)[/tex], indicating that the y-intercept [tex]\( b \)[/tex] is [tex]\(-4\)[/tex].
Thus, the slope of the function [tex]\( p(x) \)[/tex] is [tex]\(-\frac{4}{3}\)[/tex] and the y-intercept is [tex]\(-4\)[/tex].
To express the y-intercept as an ordered pair, we consider the point where the line intersects the y-axis. This occurs when [tex]\( x = 0 \)[/tex]. Substituting [tex]\( x = 0 \)[/tex] into the equation gives us:
[tex]\[ y = -4 - \frac{4}{3}(0) = -4 \][/tex]
So the y-intercept as an ordered pair is:
[tex]\[ (0, -4) \][/tex]
In summary:
- The slope is [tex]\(-\frac{4}{3}\)[/tex].
- The y-intercept is [tex]\(-4\)[/tex].
- The y-intercept as an ordered pair is [tex]\((0, -4)\)[/tex].
