To identify the slope and intercepts of the function [tex]\( f(x) = 2x \)[/tex], let's go through the steps one-by-one.
### Slope
For a linear function in the form [tex]\( f(x) = mx + b \)[/tex], the coefficient [tex]\( m \)[/tex] represents the slope of the line. In the given function [tex]\( f(x) = 2x \)[/tex], the coefficient of [tex]\( x \)[/tex] is 2.
Slope:
[tex]\[ 2 \][/tex]
### y-intercept
The y-intercept is the point where the graph of the function crosses the y-axis. This happens when [tex]\( x = 0 \)[/tex].
To find the y-intercept:
[tex]\[ f(0) = 2(0) = 0 \][/tex]
Thus, the y-intercept has coordinates [tex]\( (0, 0) \)[/tex].
y-intercept:
[tex]\[ (0, 0) \][/tex]
### x-intercept
The x-intercept is the point where the graph of the function crosses the x-axis. This happens when [tex]\( f(x) = 0 \)[/tex].
Solve for [tex]\( x \)[/tex]:
[tex]\[ 0 = 2x \][/tex]
[tex]\[ x = 0 \][/tex]
Thus, the x-intercept has coordinates [tex]\( (0, 0) \)[/tex].
x-intercept:
[tex]\[ (0, 0) \][/tex]
### Graphing the Function
1. Plot the y-intercept at [tex]\( (0, 0) \)[/tex].
2. Since the x-intercept is also at [tex]\( (0, 0) \)[/tex], this point is already plotted.
3. To draw the line, you need another point. For instance, if [tex]\( x = 1 \)[/tex]:
[tex]\[ f(1) = 2(1) = 2 \][/tex]
So, another point on the line is [tex]\( (1, 2) \)[/tex].
4. Draw a line through the points [tex]\( (0, 0) \)[/tex] and [tex]\( (1, 2) \)[/tex].
By following these steps, you will have accurately identified and graphed the linear function [tex]\( f(x) = 2x \)[/tex].
### Final Answer:
Slope: [tex]\( 2 \)[/tex]
y-intercept: [tex]\( (0, 0) \)[/tex]
x-intercept: [tex]\( (0, 0) \)[/tex]
