Question

The table shows a linear function.

Which equation represents the function.

Answer 1

`\large\boxed{f(x)=(3)/(2)x-1}`

Explanation:

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

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