The slope-intercept form of an equation is written as
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope of the line} \\ b\text{ is the y-intercept} \end{gathered}[/tex]
Given the equation
[tex]y=\frac{3-3x}{4}[/tex]
Separate the fraction so that it is expressed in two terms.
[tex]y=\frac{3-3x}{4}\Longrightarrow y=\frac{3}{4}-\frac{3x}{4}[/tex]
Swap the two position of the two terms
[tex]y=\frac{3}{4}-\frac{3x}{4}\Longrightarrow y=-\frac{3x}{4}+\frac{3}{4}[/tex]
Now that it is in the slope-intercept form, we can observe that the slope of the line is
[tex]\begin{gathered} y=-\frac{3x}{4}+\frac{3}{4} \\ \\ m=-\frac{3}{4} \\ \\ \text{Therefore, the slope of the line is }-\frac{3}{4}\text{.} \end{gathered}[/tex]
