Coordinates

Find a.

Hello Guest!

$f(x)=\frac{y_2-y_1}{x_2-x_1}\cdot(x-x_1)+y_1\\ f(x)=\frac{-5-11}{4-1}\cdot(x-1)+11\\ f(x)=-\frac{16}{3}x+\frac{16}{3}+11\\ \color{blue}y=-\frac{16}{3}x+\frac{49}{3}\ |\ \cdot 3\\ 3y=-16x+49\\ 3y+16x=49\ |\ /49\\ \frac{3}{49}y+\frac{16}{49}x=1\\ \color{blue}\frac{y}{b}+\frac{x}{a}=1$

$a=\dfrac{49}{16}$

  !