The slope-intercept form of a line is y=mx+b where m= slope and b=y-intercept.
Formula to find slope is
[tex] m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
Let's take first two points (2,3) and (3,5) to find the equation. So, plug in x1=2, y1=3, x2=3 and y2=5 in the above formula. So,
[tex] m=\frac{5-3}{3-2} [/tex]
[tex] m=\frac{2}{1} [/tex]
So, m=2
Point-slope form of a line is:
[tex] y-y_{1} =m(x-x_{1} ) [/tex]
So, next step is to plug in x1=2, y1=3 and m=2 in the above equation. Hence,
y-3=2(x-2)
y-3=2x-4
y= 2x-4+3
y=2x-1
Hence, the correct choice is D: y=2x-1
