To graph a linear function, the y and x-intercepts are always good points, then, let's find that points and do our line.
I'll start with the y-intercept because it's the easier one, it's the value of y when x = 0, then
[tex]\begin{gathered} f(x)=\frac{3}{4}x-2 \\ \\ f(0)=\frac{3}{4}\cdot0-2 \\ \\ f(0)=-2 \end{gathered}[/tex]
Then the line pass through the point (0,-2).
Now let's find the x-intercept (zero or root of the function), that's the value of x when y = 0
[tex]\begin{gathered} f(x)=\frac{3}{4}x-2 \\ \\ 0=\frac{3}{4}x-2 \\ \\ \frac{3}{4}x=2 \\ \\ x=\frac{2\cdot4}{3} \\ \\ x=\frac{8}{3} \\ \\ x=2.67 \end{gathered}[/tex]
If the point (2.67, 0) is too hard to plot, we can also use the point when x = 4
[tex]\begin{gathered} f(x)=\frac{3}{4}x-2 \\ \\ f(4)=\frac{3}{4}\cdot4-2 \\ \\ f(4)=3-2 \\ \\ f(4)=1 \end{gathered}[/tex]
A much easier point!
Plot those points:
Now do the line!
