Question

The table shows a linear function. Which equation represents the function.

Answer 1

Answer:

$\large\boxed{f(x)=\dfrac{3}{2}x-1}$

Step-by-step explanation:

$\text{The slope-intercept formula:}\\\\y=mx+b\\\\m\ -\ slope\\b\ -\ y-intercept\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{From the table we hve two points (0, -1) and (2, 2). Substitute:}\\\\m=\dfrac{2-(-1)}{2-0}=\dfrac{3}{2}$

$\text{Therefore the equation is}\ f(x)=\dfrac{3}{2}x-1\\\\\text{Check for the point (4, 5):}\\\\f(4)=\dfrac{3}{2}(4)-1=(3)(2)-1=6-1=5\qquad\ CORRECT$