Solution
1. To calculate the slope of the following equation
[tex]y=mx+c[/tex]
[tex]\begin{gathered} y=\frac{2}{3}x+10 \\ y=mx+c \\ \text{compare} \\ m=\frac{2}{3} \end{gathered}[/tex]
Slope for equation 1 = 2/3
2.
[tex]\begin{gathered} 6x+2y=5 \\ 2y=-6x+5 \\ \text{divide both side by 2} \\ \frac{2y}{2}=-\frac{6x}{2}+\frac{5}{2} \\ y=-3x+\frac{5}{2} \\ y=mx+c \\ \text{compare } \\ m=-3 \end{gathered}[/tex]
Slope for equation 2 = - 3
3. The line in the image
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ x_1=0,y_1=1 \\ x_2=-5,y_2=3 \\ \text{slope }=\frac{3-1}{-5-0}=\frac{2}{-5} \\ \text{slope = }\frac{-2}{5} \end{gathered}[/tex]
Therefore the correct slope for the equation.
1. Slope = 2/3
2. Slope = -3
3. Slope = -2/5
