Question

The equation y=20x+500 models the relationship between the number of video games, x, a company manufactures and the cost in dollars, y, to manufacture that number.

Does the equation y - 20x + 500 represent a linear function? Explain your answer.

Answer 1

Yes it is a linear function.

Explanation:

Answer 2

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.