Given equation:
[tex]-3x\text{ + 2y = 12}[/tex]
The y-intercept
The y-intercept can be found by substituting 0 for x and then solving for y:
[tex]\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}[/tex]
Answer: (0,6)
The x-intercept
The x-intercept can be found by substituting 0 for y and then solving for x
[tex]\begin{gathered} -3x\text{ + 2(0) = 12} \\ -3x\text{ = 12} \\ \text{Divide both sides by -3} \\ x\text{ = -4} \end{gathered}[/tex]
Answer: (-4,0)
the slope
The slope can be found by re-writing the equation in slope-intercept form:
[tex]\begin{gathered} y=\text{ mx + c} \\ \text{Where m is the slope} \end{gathered}[/tex]
Hence:
[tex]\begin{gathered} -3x\text{ + 2y = 12} \\ 2y\text{ = 3x + 12} \\ \text{Divide both sides by 2} \\ y\text{ = }\frac{3}{2}x\text{ + 6} \end{gathered}[/tex]
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:
