Question

The value of a share is $\$10.$ It rises steadily and reaches $\$40$ in $3$ weeks. If the weekly value of the share declines at the same rate as it increased, what will the equation for the decline in the weekly value of the share be?

• A. $y=-10x+10$
• B. $y=10x+30$
• C. $y=10x+70$
• D. $y=-10x+70$

Answer 1

The correct option is D $y=-10x+70$

Let $x$ be the number of weeks and $y$ be the value of the share in dollars.
When $x=0,y=10\text{and}x=3,y=40$
$\text{Slope}=\frac{\text{change in y-coordinate}}{\text{change in x-coordinate}}=\frac{40-10}{3-0}=\frac{30}{3}=10$
Rate of increase in the weekly value of the share = slope = $\$10$ per week

Rate of decline in the weekly value of the share = rate of increase in the weekly value of the share $=\$(-10)$ per week
$\Rightarrow \text{Slope of decline}=-10$

The equation for the declining line follows $y=mx+b$
$\Rightarrow y=-10x+b........\left(1\right)$

$(3,40)$ lies on the declining line.
Substituting $x=3,y=40$ in equation (1), we get
$\Rightarrow 40=-10$x$3$+$b$
$\Rightarrow 40=-30+b$
$\Rightarrow b=40+30$
$\Rightarrow b=70$

Hence, the equation for the rate of decline in the weekly value of the share
$\Rightarrow y=-10x+70$