Question

6 linear function x f(x) -6 -10 -2 -4 4 5 10 14 what is the equation of function f in slope - intercept form? move the correct answer to each box. not all answers will be used. $-\frac{3}{2}$ 1 $\frac{1}{2}$ 1 $\frac{3}{2}$ $\frac{7}{4}$ $f(x)=square x+square$

Explanation:

Step1: Find the slope (m)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Let's use the points \((-6, -10)\) and \((-2, -4)\).
\( m=\frac{-4 - (-10)}{-2 - (-6)}=\frac{-4 + 10}{-2 + 6}=\frac{6}{4}=\frac{3}{2} \)

Step2: Find the y - intercept (b)

Use the slope - intercept form \( y=mx + b \) and a point, say \((-2, -4)\) with \( m=\frac{3}{2} \).
Substitute into the formula: \(-4=\frac{3}{2}(-2)+b\)
Simplify: \(-4=-3 + b\)
Solve for \( b \): \( b=-4 + 3=-1 \)

Step3: Write the equation

The slope - intercept form is \( f(x)=mx + b \), so \( f(x)=\frac{3}{2}x-1 \)

Answer:

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