Given equation
[tex]y=2x+6\ldots(1)[/tex]
put x = 0 in equation (1) we get,
[tex]\begin{gathered} y=2(0)+6 \\ y=0+6 \\ y=6 \end{gathered}[/tex]
put x = 1 in equation (1) we get,
[tex]\begin{gathered} y=\text{ 2(1)+6} \\ y=\text{ 2+6} \\ y=8 \end{gathered}[/tex]
put x = -2 in equation (1) we get,
[tex]\begin{gathered} y=\text{ 2(-2) +6} \\ y=-4+6 \\ y=2 \end{gathered}[/tex]
put x = 2 in the equation (1) we get,
[tex]\begin{gathered} y=\text{ 2(2)+6} \\ y=\text{ 4+6} \\ y=\text{ 10} \end{gathered}[/tex]
The table will look like this,
to find the x intercept put y= 0 in the equation (1) and to find y intercept put x = 0 in the quation (1) we get ,
x - intercept = (-3,0)
y - intercept = (0,6)
to find the slope we use the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
consider two points , say (0,6) and (1,8)
[tex]\begin{gathered} x_1=0,y_1=6 \\ x_2=1,y_2=8 \end{gathered}[/tex]
Now, subsitute the above values in slope formula we get,
[tex]\begin{gathered} m=\frac{8-6}{1-0} \\ m=2 \end{gathered}[/tex]
Thus, slope is 2
