Question

Hari’s weekly allowance varies depending on the number of chores he does. He received $16 an alarm once a week he did 12 chores, and $14 in allowance the week he did 8 chores. Write an equation for his allowance in slope-intercept form.

Answer 1

Answer:

y = ($0.5/ch) x + $10

Step-by-step explanation:

Let

x = number of chores

y = allowance

The relationship between y and x can be expressed in a linear equation in the slope-intercept form.

y = mx + b

where

m is the slope

b is the y-intercept

We have the ordered pairs (8, 14) and (12, 16). We can calculate the slope using the following expression.

m = Δy/Δx = $16-$14/12ch-8ch = $0.5/ch

The equation is

y = ($0.5/ch) x + b

We will replace the first point in the previous equation.

$14 = ($0.5/ch) 8ch + b

b = $10

The final equation is

y = ($0.5/ch) x + $10

Answer 2

$\bf \begin{array}{ccll} chores&\stackrel{weekly}{allowance}\\ \cline{1-2} 12&16\\ 8&14 \end{array}~\hspace{10em} (\stackrel{x_1}{12}~,~\stackrel{y_1}{16})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{14}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{14-16}{8-12}\implies \cfrac{-2}{-4}\implies \cfrac{1}{2}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-16=\cfrac{1}{2}(x-12) \\\\\\ y-16=\cfrac{1}{2}x-6\implies y=\cfrac{1}{2}x+10$