linear equation

Question

the population of spring city was 15,000 in 1990, and 7250 in 2000. Create a linear equation to represent this situation. According to your equation, what will the population be in the year 2006?

Answer 1

Hi Kimberly,

In the real world, most population growth scenarios are usually expressed as an exponential equation/function, but in this case, we are using a linear model. Thus, you will use the slope equation to find the rate of change as follows:

m = (y₂ - y₁) ÷ (x₂ - x₁)

m = (7250 - 15000) ÷ (2000 - 1990) → -7750/10 = -775

Next, you will apply the point-slope formula: (y - y₁) = m(x - x₁) using the data above, you will get the following equation.

(y - 15000) = -775(x - 1990)

Lastly, you can convert this expression into its slope-intercept form using algebraic manipulation to get the following:

y -15000 = -775x + 1542250

y = -775x + 1557250

This final expression can be inputted into graphing calculator or Desmos online graphing app to show the visual; however, you will need to change the windows/display settings to see the picture according to scale.

Regards,

Lance