Question

Find the gradient and the $$y$$-intercept of the following lines:

$$\frac{x}{6} + \frac{y}{9} = 1$$

Answer 1

A linear equation in slope-intercept form is $$y = mx + c$$, where $$m$$ is the gradient (slope) and $$c$$ is the $$y$$-intercept.

$$\frac{x}{6} + \frac{y}{9} = 1$$:

$$\frac{y}{9} = -\frac{x}{6} + 1$$

$$y = -\frac{9}{6}x + 9$$ 

$$= -\frac{3}{2}x + 9$$

Therefore, gradient $$m = -\frac{3}{2}$$ and $$y$$-intercept $$c = 9$$.