Question

Help please ;-; The values in the table represent a linear function.

Answer 1

Answer:

The function rule in slope-intercept form is:

$y = \frac{1}{2}x-\frac{7}{2}$

Step-by-step explanation:

The slope-intercept form of a function is given as:

$y = mx+b$

Here

m is the rate of change of function and b is the y-intercept

The rate of change is calculated as:

$m = \frac{difference\ in\ y}{difference\ in\ x}$

For this, any two pairs of input and output can be taken.

So using the pairs (1,-3) and (2,-1)

$m=\frac{2-1}{-1+3}\\=\frac{1}{2}$

Putting the value of slope in slope-intercept form

$y = \frac{1}{2}x+b$

Putting (1,-3) in the equation

$-3 = \frac{1}{2}(1)+b\\-3 = \frac{1}{2}+b\\b = -3-\frac{1}{2}\\b = \frac{-6-1}{2}\\b= \frac{-7}{2}$

Putting the value of b

$y = \frac{1}{2}x-\frac{7}{2}$

Hence,

The function rule in slope-intercept form is:

$y = \frac{1}{2}x-\frac{7}{2}$