We are given the following equation
[tex]3x-2y=12[/tex]
A. x-intercept
The x-intercept is the point where the line intersects the x-axis.
It can be found by substituting y = 0 into the equation.
[tex]\begin{gathered} 3x-2y=12 \\ 3x-2(0)=12 \\ 3x=12 \\ x=\frac{12}{3} \\ x=4 \end{gathered}[/tex]
Therefore, the x-intercept is 4
x-intercept = (4, 0)
B. y-intercept
The y-intercept is the point where the line intersects the y-axis.
It can be found by substituting x = 0 into the equation.
[tex]\begin{gathered} 3x-2y=12 \\ 3(0)-2y=12 \\ -2y=12 \\ y=\frac{12}{-2} \\ y=-6 \end{gathered}[/tex]
Therefore, the y-intercept is -6
y-intercept = (0, -6)
C. Slope
Recall that the slope-intercept form of an equation is given by
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
Let us convert the given equation into the above slope-intercept form.
[tex]\begin{gathered} 3x-2y=12 \\ -2y=-3x+12 \\ y=\frac{-3x+12}{-2} \\ y=\frac{-3x}{-2}+\frac{12}{-2} \\ y=\frac{3}{2}x-6 \end{gathered}[/tex]
Comparing the above equation with the slope-intercept form, we see that the slope is 3/2
Slope = 3/2
