The equation to graph is:
[tex]y=-\frac{3}{2}x+3[/tex]Let's break it down and see how can we EASILY graph this!!
The first point is to always put x = 0 and find the y-value. This way, we graph the y-intercept. Thus,
[tex]\begin{gathered} y=-\frac{3}{2}x+3 \\ y=-\frac{3}{2}(0)+3 \\ y=3 \end{gathered}[/tex]So, y-intercept is (0, 3).
Now, look at the slope, the constant before "x". It is -3/2.
The numerator is rise and denominator is run.
Thus, from the y-intercept, we move "-3" units "rise" (y-direction) and "2" units "run" (x-direction).
We will arrive at (2,0).
Then we can make this move again!
We will arrive at (4, -3).
That's it!!
We can now graph the 3 points found, draw a smooth line through these points and that's our line!!
The graph of the line is shown below:
