Answer :
The slope-intercept equation from the two-point form is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex][tex]x_{1_{}}=1,y_1=4,x_2=2,y_2=\text{ 6}[/tex][tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-\text{ 4 =}\frac{6-4}{2-1}(x\text{ - 1)} \end{gathered}[/tex][tex]\begin{gathered} y\text{ - 4 = }\frac{2}{1}(x-1) \\ y-4\text{ = 2(x-1)} \\ y-4=2x-2 \\ \text{collect like terms} \\ y=2x\text{ -2 +4} \\ y\text{ = 2x + 2} \end{gathered}[/tex]The equation is y = 2x + 2
From y = mx + c
m = 2, c = 2
m is the slope, while c is the intercept on the y-axis
[tex]\begin{gathered} \text{the slope m} \\ m\text{ =}\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex][tex]\begin{gathered} m\text{ = }\frac{6-4}{2-1}=\frac{2}{1}=2 \\ m\text{ = 2} \end{gathered}[/tex]