Step-by-step explanation:
This is the standard linear equation:
[tex]y=mx+b[/tex]
[tex]m[/tex] represents slope and [tex]b[/tex] represents the y-intercept. In a finished equation, [tex]x[/tex] and [tex]y[/tex] are left as variables. [tex]x[/tex] and [tex]y[/tex] represent any given point in the function. In this case, one of the given coordinates is [tex](-8, 6)[/tex], and we can use this by using [tex]-8[/tex] as [tex]x[/tex] and [tex]6[/tex] as [tex]y[/tex]. After plugging in known variable, the equation becomes this:
[tex]6 = \frac{1}{4} ( - 8) + b[/tex]
This simplifies to:
[tex]6 = - 2 + b[/tex]
Then to:
[tex]4=b[/tex].
After plugging in slope and y-intercept, the finished equation is:
[tex]y = \frac{1}{4} x + 4[/tex]
