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In two dimensions:
A straight line that crosses the y-axis at y=c and has gradient m, has equation y=mx+c.
The straight line that passes through points (a,b) and (c,d) has equation (x-a)/(x-c)=(y-b)/(y-d).
In three dimensions:
A straight line that passes through points (a,b,c) and (d,e,f) has equation (x-a)/(x-d)=(y-b)/(y-e)=(z-c)/(z-f).
A line's equation can also be written y=mx+c, z=nx+d. This line intersects the y,z plane at y=c, z=d.