Given: The equation below
[tex]y=-\frac{2}{3}x+3[/tex]To Determine: The graph representing the equation using the slope and y-intercept
Solution
Step 1: Determine the y-intercept
To calculate the y-intercept, make x = 0
[tex]\begin{gathered} y=-\frac{2}{3}x+3,x=0 \\ y=-\frac{2}{3}(0)+3 \\ y=0+3 \\ y=3 \end{gathered}[/tex]The coordinate of the y-intercept is (0, 3)
Step 2: Determine the x-intercept
To calculate the x-intercept, make y = 0
[tex]\begin{gathered} y=-\frac{2}{3}x+3,y=0 \\ 0=-\frac{2}{3}x+3 \\ \frac{2}{3}x=3 \\ 2x=3\times3 \\ 2x=9 \\ x=\frac{9}{2} \\ x=4.5 \end{gathered}[/tex]The coordinate of the x-intercept is (4.5, 0)
Step 3: Determine the slope
The general equation of a straight line is given as
[tex]\begin{gathered} y=mx+c \\ m=\text{slope} \\ c=y-\text{ intercept} \end{gathered}[/tex]Compare the general equation to the given equation
[tex]\begin{gathered} y=-\frac{2}{3}x+3 \\ y=mx+c \\ slope(m)=-\frac{2}{3} \end{gathered}[/tex]Use the coordinates of y-axis, x-axis and the slope to plot graph as shown below
