For question number one, we have four points:
(2,12), (4,16), (8,24) and (10,28)
In order to find the slope, we need two of them. I'll choose the (2,12) and (4,16) (could be any combination of two points).
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x} \\ m=\frac{16-12}{4-2} \\ m=\frac{4}{2} \\ m=2 \end{gathered}[/tex]
So, the slope of this line, m, is 2.
Now for the equation, using the point (8,24) (again, it could be any of them);
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-24=2(x-8) \\ y=2x-16+24 \\ y=2x+8 \end{gathered}[/tex]
y = 2x +8 is the slope-intercept form of the equation of the line. The slope is 2 and the y-intercept is 8.
