Question

Find the slope of 1/2x+1/3y=1

Answer 1

We want to determine the slope of the equation;

`(1)/(2)x+(1)/(3)y=1`

We need to express the equation in the slope-intercept form;

`y=mx+c`

where m is the slope and c is the intercept.

Firstly, let's multiply the equation through by 3;

`\begin{gathered} (1*3)/(2)x+(1*3)/(3)y=1*3 \\ (3)/(2)x+y=3 \end{gathered}`

Then, let's subtract (3/2)x from both sides;

`\begin{gathered} (3)/(2)x-(3)/(2)x+y=3-(3)/(2)x \\ y=-(3)/(2)x+3 \end{gathered}`

comparing the resulting equation to the slope-intercept form of straight line equation, then the slope is the coefficient of x;

`slope(m)=-(3)/(2)`

The slope of the line is -3/2