Regression - slope doubt

Question

The gradient of the regression line $x$ on $y$ is $-0.2$ and the line passes through $(0,3)$. If the equation of the line is $x = c + dy$, find the value of $c$ and $d$.

What I did: As per my understanding, gradient is the slope and therefore the value of $d = -0.2$. Substituting that in the equation, I get $c = 0.6$.

The book's answer is $c = 15$ and $d = -5$. How?

Answer 1

We have $y=\frac{x}{d}-\frac{c}{d}$, thus $\frac{1}{d}=-0.2$ and $d=-5$. Now plugging in $(0,3)$ yields $3=\frac{0}{-5}-\frac{c}{-5}=\frac{c}{5}$, thus $c=15$. The line you are using is of the form $x=c+dy$, but to use your standard method you want to work with a line of the form $y=ax+b$, and thus you have to first rewrite $x=c+dy$ to an equation where $y$ is the variable on the left hand side.

Answer 2

The gradient show the slope as $\frac{\Delta y}{\Delta x}$. Note that your equation is not $y=ax+b$ but $x=c+dy$. I can look at the first equation and rewrite is as $$x=\frac{1}{a}y-\frac{b}{a}$$ Therefore if you are given $a=-0.2$, you get $d=\frac{1}{a}=\frac{1}{-0.2}=-5$