Question

find the equation of the linear function represented by the table below in slope-intercept form. picture of table is below

Answer 1

`y = 3x + 2`

Explanation:

The equation of a linear function in slope-intercept form is: y = mx + b, where, m = slope, and b = y-intercept.

Find slope (m) of the linear function by using any two points, say (3, 11) and (7, 23):

`m = (y_2 - y_1)/(x_2 - x_1) = (23 - 11)/(7 - 3) = (12)/(4) = 3`

To find the y-intercept (b), substitute the value of the corrdinate pair of any of the points represented on the table, and the value of the slope (m) into
`y = mx + b`.

Substituting, x = -1, y = -1, m = 3.

`y = mx + b`

`-1 = 3(-1) + b`

`-1 = -3 + b`

Add 3 to both sides

`-1 + 3 = b`

`2 = b`

`b = 2`

Substitute m = 3, and b = 2 into the equation of the linear function in slope-intercept form:

`y = mx + b`

`y = 3x + 2`