Question

Find the gradient of 3(x-2y)=2

Answer 1

The equation given is a linear equation, so its gradient is the same as the slope of the line.

If the line is in the slope-intercept form:

$y=sx+b$

"s" is the slope and, thus, the gradient.

So, we can solve the equation for "y" and check the coefficient multiplying "x":

$\begin{gathered} 3(x-2y)=2 \\ 3x-6y=2 \\ 3x-2=6y \\ 6y=3x-2 \\ y=\frac{3}{6}x-\frac{2}{6} \\ y=\frac{1}{2}x-\frac{1}{3} \end{gathered}$

The coefficient multiplying x is 1/2, so the gradient is 1/2.