Question

u.s. population
a 3x + 150
b 18x + 235
c 5x + 236
d 13x + 270

Explanation:

Step1: Estimate the \(y -\)intercept

The \(y -\)intercept (\(x = 0\)) is close to \(235\).

Step2: Estimate the slope

Take two points \((x_1,y_1)=(1,248)\) and \((x_2,y_2)=(4,265)\).
Slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{265 - 248}{4 - 1}=\frac{17}{3}\approx6\).
Check the formula \(y=mx + b\).
For \(y = 18x+235\), when \(x = 1\), \(y=18\times1 + 235=253\) (too large).
For \(y = 5x+236\), when \(x = 1\), \(y=5\times1+236 = 241\); when \(x = 4\), \(y=5\times4+236=256\).
For \(y = 3x+150\), when \(x = 1\), \(y=3\times1+150 = 153\) (too small).
For \(y = 13x+270\), when \(x = 1\), \(y=13\times1+270=283\) (too large).

Answer:

C. \(5x + 236\)