Question

10. Yasin's father increases his allowance each year on his birthday. His allowance was $5 a week when he was 8 and $12.50 a week when he was 11. What is Yasin's weekly allowance when he is 14?

Answer 1

$\mathrm{Line\:passing\:through\:}\left(8,\:5\right)\mathrm{,\:}\left(11,\:12.5\right)$

$\dpi{200} \tiny \mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\left [ \left(x_1,\:y_1\right)=\left(8,\:5\right),\:\left(x_2,\:y_2\right)=\left(11,\:12.5\right) \right ]$

$\dpi{200} \tiny m=\frac{12.5-5}{11-8}=2.5$

$\dpi{200} \tiny \mathrm{Plug\:the\:slope\:}2.5\mathrm{\:into\:}y=mx+b$

$\dpi{200} \tiny \mathrm{Plug\:in\:}\left(8,\:5\right)\mathrm{:\:}\quad \:x=8,\:y=5$

$\dpi{200} \tiny 5=2.5\cdot \:8+b$

$\dpi{200} \tiny b=-15$

$\dpi{200} \tiny \mathrm{Construct\:the\:line\:equation\:}\mathbf{y=mx+b}\mathrm{\:where\:}\mathbf{m}=2.5\mathrm{\:and\:}\mathbf{b}=-15$

$\dpi{200} \tiny y=2.5x-15$

Substitute x =14

y= 2.5 *14 -15

y=35 -15

y =20

hence, allowance is $20