Question

What is the y-intercept of the function f(x) = –f(x) equals negative StartFraction 2 Over 9 EndFraction x plus StartFraction 1 Over 3 EndFraction.x + ?

–negative StartFraction 2 Over 9 EndFraction.
–negative StartFraction 1 Over 3 EndFraction.
StartFraction 1 Over 3 EndFraction.
StartFraction 2 Over 9 EndFraction.

Answer 1

Answer: Third option

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope of the line and "b" is the y-intercept.

Given the function f(x):

$f(x)=-\frac{2}{9}x+\frac{1}{3}$

Since $f(x)=y$, you can rewrite it:

$y=-\frac{2}{9}x+\frac{1}{3}$

You can identify that:

$m=-\frac{2}{9}\\\\b=\frac{1}{3}$

Therefore, you can determine that the y-intercept of the given function is:

$b=\frac{1}{3}$

Observe that this matches with the third option.

Answer 2

The y-intercept of the function is $\frac{1}{3}$

The standard equation of a line in slope-intercept form is expressed as;

$y = mx + b$ where:

m is the slope

b is the intercept

Given the function that represents the equation of a line as:

$f(x) =- \frac{2x}{9} +\frac{1}{3}$

Comparing the given equation with the standard;

$mx = -\frac{2}{9}x\\m = = -\frac{2}{9}$

Similarly;

$b= \frac{1}{3}$

This shows that the y-intercept of the function is $\frac{1}{3}$

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