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Identify the slope and intercepts of the function [tex]f(x)=2x[/tex]. Write DNE if they don't exist. Then graph the equation in the coordinate system by clicking on the ordered pair associated with the intercept and then lead the line through another point of your choosing.

Function: [tex]f(x)=2x[/tex]

1. Slope:
[tex]\boxed{\text{Slope}}[/tex]

2. [tex]y[/tex]-intercept (write its coordinates):
[tex]\boxed{\text{( }0, 0\text{ )}}[/tex]

3. [tex]x[/tex]-intercept (write its coordinates):
[tex]\boxed{\text{( }0, 0\text{ )}}[/tex]

Sagot :

GinnyAnsweridn
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]
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