The normal meaning for this standard linear equation is that x and y are coordinates in a rectangular arrangement of axes. The y axis is North-South while the x axis is East-West. Where they cross is called the origin with coordinates (0,0), that is, x and y are both zero. The equation y=mx+b defines a straight line. It slopes at a value given by m, the slope or gradient, and m is a number which can be a whole number, a fraction, or whatever, as long as it is constant so that the line remains straight.
The slope, m, is also known as the tangent, and the tangent of the angle that the line makes with the x axis has a value of m. When the straight line is at an angle of 45 degrees to the x axis, its tangent is 1 so m=1. If the line slopes backwards at 45 degrees to the x axis, it's tangent is -1 and m=-1. Forward sloping lines have a positive m, while backward sloping lines have a negative m.
The value of b is also called the y intercept, because it's the point on the y axis where the straight line crosses that axis. It can have a positive or negative value. b is a constant, just like m.
mx is m times x. The x axis is divided by equally spaced numbers, 0, 1, 2, 3 etc to the right, and -1, -2, -3 etc to the left of the origin. The y axis is similarly divided, postitive numbers going up and negative numbers going down. By putting numbers in the equation you can work out where points go on the line. m will have a value, like 2, for example, and b a value, say, 3, so we have y=2x+3. If we put x=0 we get y=3 which is the y intercept. So we mark that point (0,3) by going up 3 divisions on the y axis. Now put x=1, then y=5. So we move to the point (1,5), which is right 1 and up 5. We can join that point to (0,3) and continue beyond these points. What we find is that, although we have only plotted two points, other values of x and y actually fit on the line. If we look at where x=3 and go up to meet the line, then go horizontally back to the y axis, we should find it meets the point 9 on the y axis. So the line represents the relationship between x and y as given by the equation for all points including points in between our whole number divisions, like, for example, 1.5 or one and a half, halfway between 1 and 2.
