Question

the table represents the change in ( f(x) ) for given values of ( x ).

( x )	( f(x) )
( -1 )	( -5\frac{2}{5} )
( 0 )	( -6 )
( 1 )	( -6\frac{3}{5} )
( 2 )	( -7\frac{1}{5} )

a ( f(x) = x - \frac{3}{5} )
b ( f(x) = -\frac{3}{5}x - 6 )
c ( f(x) = -\frac{5}{3}x + 6 )
d ( f(x) = x - 6 )
e ( f(x) = x - \frac{2}{5} )

Explanation:

Step1: Find the slope (m)

Use two points, e.g., \((0, -6)\) and \((1, -6\frac{3}{5})\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-6\frac{3}{5}-(-6)}{1 - 0}=\frac{-\frac{3}{5}}{1}=-\frac{3}{5}\).

Step2: Identify the y-intercept (b)

When \(x = 0\), \(f(x)=-6\), so \(b=-6\).

Step3: Write the equation

Using the slope - intercept form \(f(x)=mx + b\), substitute \(m = -\frac{3}{5}\) and \(b=-6\). So \(f(x)=-\frac{3}{5}x-6\).

Answer:

B. \(f(x)=-\frac{3}{5}x - 6\)