Question

population of webb county, texas
the population of webb county, texas, from the year 2000 through 2010 is shown in the graph. if the trend shown in the graph continues, what will be the population of webb county in 2015?
use the slope to help you!
(circ) 307,000
(circ) 278,500
(circ) 471,500
(circ) 158,000

Explanation:

Step1: Calculate slope of the line

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
Using points $(0,193)$ and $(10,250)$:
$m = \frac{250 - 193}{10 - 0} = \frac{57}{10} = 5.7$

Step2: Define linear population model

Linear equation: $y = mx + b$
$b=193$ (y-intercept), so $y = 5.7x + 193$

Step3: Find x for 2015

Years since 2000: $x = 2015 - 2000 = 15$

Step4: Calculate 2015 population

Substitute $x=15$ into the equation:
$y = 5.7(15) + 193 = 85.5 + 193 = 278.5$
This value is in thousands, so multiply by 1000: $278.5 \times 1000 = 278500$

Answer:

278,500