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musiclover10045

Find the slope of the line by using two points on the line.

Using (0,-2) and (3,0)

The slope is the change in Y over the change in x:

Slope = (0 - -2) / (3-0) = 2/3

The y intercept is where the line crosses Y at  = 0, from the picture when X is 0 the line crosses at -2.

The equation becomes 2/3x -2

The answer is: f(x)=2/3x−2

SociometricStar

Answer:

[tex]f(x)=\frac{2}{3}-2[/tex]

First option is correct.

Step-by-step explanation:

The intercept form of a line is given by

[tex]\frac{x}{a}+\frac{y}{b}=1[/tex]

Here a is the x-intercept and b is the y-intercept.

From the given graph,

x-intercept = 3

y-intercept = -2

Hence, we have

a = 3 and b = -2

Substituting these values in above equation

[tex]\frac{x}{3}+\frac{y}{-2}=1\\\\\frac{x}{3}-\frac{y}{2}=1\\\\\frac{y}{2}=\frac{x}{3}-1\\\\y=\frac{2}{3}-2[/tex]

Hence, the function rule for the line is given by

[tex]f(x)=\frac{2}{3}-2[/tex]

First option is correct.

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