Question

Identify the slope and y-intercept of equation 4x+3y=12

Answer 1

Hello there. To solve this question, we'll have to remember some properties about the equation of a line.

Given the equation:

`4x+3y=12`

We have to determine the slope and the y-intercept of this line.

For this, the best way to start is to find the equation of the line in slope-intercept form. It is given by:

`y=mx+b`

Where m is the slope of the line and b is the y-intercept.

To do so, we simply have to solve the equation for y.

Start subtracting 4x on both sides of the equation:

`\begin{gathered} 4x+3y-4x=12-4x \\ 3y=12-4x \end{gathered}`

Divide both sides of the equation by a factor of 3

`\begin{gathered} (3y)/(3)=(12-4x)/(3) \\ \\ y=4-(4)/(3)x \end{gathered}`

Comparing it to the slope-intercept form of the line, we find that:

`\begin{gathered} m=-(4)/(3) \\ b=4 \end{gathered}`

These are the slope and the y-intercept of the equation.