Question

This graph gives the growth of a plant over time.
What is the slope of the line, and what does the slope mean in
this situation?
Select from the drop-down menus to correctly complete the
statement
The slope is Choose
Choose by Choose
&
which means that the plant
✓every day
Growth (in.)
10
9
84
7
4
3
(2, 1)
(0,0)0 12
Growth vs. Time
(4,2)
(7,3.5)
Time (days)
9 10
2 3 4
5 6
Next >>
AK12

Answer 1

to get the slope of any straight line, we simply need two points off of it, let's use the points in the picture below

$(\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{3.5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\LARGE inches}}{\stackrel{rise} {\stackrel{y_2}{3.5}-\stackrel{y1}{2}}}}{\underset{\textit{\LARGE days}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{4}}}} \implies \cfrac{1.5}{3}\implies \cfrac{1}{2} ~~ \cfrac{inch}{day}\qquad \begin{array}{llll} \textit{the plant is growing}\\ \textit{1 inch every 2 days} \end{array}$

Answer 2

Answer:

$\textsf{The slope is \boxed{\dfrac{1}{2}} which means that the plant}$

$\textsf{ \boxed{\sf grows} by \boxed{\dfrac{1}{2}\; \sf inch} every day}.$

Step-by-step explanation:

$\boxed{\begin{minipage}{4.4cm}\underline{Slope Formula}\\\\Slope (m)=\dfrac{y_2-y_1}{x_2-x_1} \\\\where (x_1,y_1) and (x_2,y_2) \\are two points on the line.\\\end{minipage}}$

Define two points on the line:

• Let (x₁, y₁) = (2, 1)
• Let (x₂, y₂ = (4, 2)

Substitute the defined points into the slope formula to find the slope:

$\implies \textsf{slope}\:(m)=\dfrac{2-1}{4-2}=\dfrac{1}{2}$

The slope is the rate at which the plant grows per day.

Solution

$\textsf{The slope is \boxed{\dfrac{1}{2}} which means that the plant}$

$\textsf{ \boxed{\sf grows} by \boxed{\dfrac{1}{2}\; \sf inch} every day}.$