Explanation:
yes,
y = 20x + 500
is a typical linear function.
we have a linear function, when the ratio (y2 -y1)/(x2 - x1) is constant for any pair of points on the graph of the function. thus is also called the slope.
let's say, we use x = 0, x = 10, x = 20 with the corresponding y = 500, y = 700, y = 900 s the past of points
(0, 500) and (10, 700)
(10, 700) and (20, 900)
in the first case
x changes by +10 (from 0 to 10).
y changes by +200 (from 500 to 700).
the slope is between these 2 points +200/+10 = 20.
in the second case we have
x changes by +10 (from 10 to 20).
y changes by +200 (from 700 to 900).
the slope is between these 2 points +200/+10 = 20.
they are equal.
so, we see, the slope is constant along the whole function.
thus, the graph is a straight line. hence the name : it is a linear function.
remember, when the exponent of the variable (x in our case) is 1, then you have a linear equation.
x² (exponent 2 or higher) or 1/x (exponent -1 or lower) or sqrt(x) (exponent 1/2 or other fractions) or other forms of x that are not x¹ create bent curves, and are therefore not linear.