Question

For the equation -3x + 2y = 12, find the following-

Answer 1

Given equation:

`-3x\text{ + 2y = 12}`

The y-intercept

The y-intercept can be found by substituting 0 for x and then solving for y:

`\begin{gathered} -3(0)\text{ + 2y = 12} \\ 0\text{ + 2y =12} \\ 2y\text{ = 12} \\ Divide\text{ both sides by 2} \\ y\text{ = 6} \end{gathered}`

Answer: (0,6)

The x-intercept

The x-intercept can be found by substituting 0 for y and then solving for x

`\begin{gathered} -3x\text{ + 2(0) = 12} \\ -3x\text{ = 12} \\ \text{Divide both sides by -3} \\ x\text{ = -4} \end{gathered}`

Answer: (-4,0)

the slope

The slope can be found by re-writing the equation in slope-intercept form:

`\begin{gathered} y=\text{ mx + c} \\ \text{Where m is the slope} \end{gathered}`

Hence:

`\begin{gathered} -3x\text{ + 2y = 12} \\ 2y\text{ = 3x + 12} \\ \text{Divide both sides by 2} \\ y\text{ = }(3)/(2)x\text{ + 6} \end{gathered}`

Answer:

slope = 3/2

The graph of the line can be obtained by joining two points using a straight line.

We have the points (0,6) and (-4,0)

Hence, the graph of the line is: