As Shaktal points out "The general equation for a straight line in Cartesian co-ordinates is y=mx+c, where m is the gradient of the straight line and c is the y-intercept of the line."
So you need to find the gradient or slope 'm' and the y-interecpt 'c', in other words the value of y where x=0.
To find the gradient, since the equation is linear, you can take any two points (a, b) and (c, d) and calculate
(d-b) -----=m (c-a)
Then once you have that number m, you can take any point (x, y) and write y=mx+c. Then you can figure out the value of c such that this equation holds true.
As an example say you have (1, 4) and (2, 10) as the points for which you want to find a linear equation. m=(6/1)=6. Then considering (2, 10) we can write 10=(6)(2)+c or 10=12+c. So, c=-2, and our linear equation reads y=6x-2.
If you hand-plot the points, draw out your co-ordinate system, plot the points, and then connect them with a ruler or straight edge.