Question

height (inches) child growth rate (after birth) months y 0 20 40 0 4 8 x (1, 15) (6, 30) r benchmark extra credit an equation of the line and interpret the slope and y - intercept. 2. speed (mi/h) walking time (hours) y 0 2 4 0 2 4 x (2, 3) (4, 3)

Explanation:

Step1: Find the slope ($m$)

Use the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(1,15)$ and $(x_2,y_2)=(6,30)$.
$$m=\frac{30 - 15}{6 - 1}=\frac{15}{5}=3$$

Step2: Find the y - intercept ($b$)

Use the point - slope form $y - y_1=m(x - x_1)$. Substitute $m = 3$, $x_1 = 1$, $y_1 = 15$.
$y-15=3(x - 1)$
$y-15=3x-3$
$y=3x + 12$

Answer:

The equation of the line is $y = 3x+12$. The slope $m = 3$ means the child's height increases by 3 inches per month. The y - intercept $b = 12$ means the child's height at birth (when $x = 0$ months) is 12 inches.