Question

Linear equation in slope intercept form

Answer 1

Given:

The table of values of a linear function.

To find:

The equation of linear function in slope intercept form.

Solution:

The slope intercept form of a linear function is:

`y=mx+b`

Where, m is the slope and b is the y-intercept.

If a linear function passes through two point, then the equation of the linear function is:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Consider any two points from the given table. Let the two points are (-6,12) and (-5,14). So, the equation of the linear function is:

`y-12=(14-12)/(-5-(-6))(x-(-6))`

`y-12=(2)/(-5+6)(x+6)`

`y-12=(2)/(1)(x+6)`

`y-12=2x+12`

Adding 12 on both sides, we get

`y-12+12=2x+12+12`

`y=2x+24`

Therefore, the slope intercept form for the given linear function is
`y=2x+24`.