Question

for linear function f, f(-3) = 0 and f(5) = -4. complete function f in slope-intercept form. move the correct answer to each box. not all answers will be used. -3 -2 -1.5 -0.5 0.5 1.5 2 3 f(x) = \boxed{}x + \boxed{}

Explanation:

Step1: Find the slope \( m \)

The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( f(-3)=0 \) means the point is \( (-3, 0) \) and \( f(5)=-4 \) means the point is \( (5, -4) \). So, \( x_1=-3, y_1 = 0, x_2 = 5, y_2=-4 \).
\( m=\frac{-4 - 0}{5 - (-3)}=\frac{-4}{8}=-\frac{1}{2}=-0.5 \)

Step2: Find the y - intercept \( b \)

The slope - intercept form of a line is \( y=mx + b \) (or \( f(x)=mx + b \)). We know \( m=-0.5 \) and we can use the point \( (-3, 0) \) to find \( b \). Substitute \( x=-3 \), \( y = 0 \) and \( m=-0.5 \) into \( f(x)=mx + b \):
\( 0=-0.5\times(-3)+b \)
\( 0 = 1.5 + b \)
Subtract \( 1.5 \) from both sides: \( b=0 - 1.5=-1.5 \)

Answer:

\( f(x)=\boxed{-0.5}x+\boxed{-1.5} \)