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:
[tex]y=mx+b[/tex]
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:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
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:
[tex]y-12=\dfrac{14-12}{-5-(-6)}(x-(-6))[/tex]
[tex]y-12=\dfrac{2}{-5+6}(x+6)[/tex]
[tex]y-12=\dfrac{2}{1}(x+6)[/tex]
[tex]y-12=2x+12[/tex]
Adding 12 on both sides, we get
[tex]y-12+12=2x+12+12[/tex]
[tex]y=2x+24[/tex]
Therefore, the slope intercept form for the given linear function is [tex]y=2x+24[/tex].
