Question

A pea plant grows $0.5$ inches per day. After $6$ days, the height of the pea plant is $12$ inches.
The given graph shows the height of the pea plant $\left(h\right)$ recorded over a number of days $\left(d\right).$
Write the equation for the given graph.

• A. $y=0.5x+9$
• B. $y=9x+0.5$
• C. $2y=9y+0.5$
• D. $2y=0.5x+9$

Answer 1

The correct option is A $y=0.5x+9$

Let the initial height of the pea plant be $h$.
Rate at which pea plant grows $=$ slope $\left(m\right)=0.5$ in per day
We can see that the coordinates of point $A$ and point $B$ in the graph are $A(2,10)$ and $B(6,12).$

The equation of the line is
$y=mx+b,$ where $b$ is the $y$-intercept.
When $x=2,y=10,$ and $x=6,y=12,$
We find the value of $b$ by substituting the value of $x$ and $y$ in the equation of line.

$10=0.5\times 2+b$
$\Rightarrow 10=1+b$
$\Rightarrow b=10-1$
$\Rightarrow b=9$
Hence, the equation of line is $y=0.5x+9$