The equation of a linear function is given by the following general form:
y = mx + b
Where m is the slope of the line and is given by the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Where (x1, y1) and (x2, y2) are two points of the function. In this case, we can take points (3, 0) and (4, 6) from the table, then we get:
[tex]m=\frac{6-0}{4-3}=\frac{6}{1}=6[/tex]With m = 6 we can rewrite the equation like this:
y = 6x + b
By replacing another point, like (5, 12), we get:
12 = 6(5) + b
12 = 30 + b
12 - 30 = 30 - 30 + b
-18 = b
b = -18
Then, the equation of the linear function can be written like this:
h(x) = 6x - 18