Y=2X+3 Help understanding Gradients?

The y value is the value which depends on the x value so as you change x by one unit y will change by 2 units.The gradient is the ratio of rise/horizontal run (in trigonometry this is known as a tangent).It is the result of dividing one number(the change in y) by another(the change in x) so the answer is 2 and you are correct.But it is not a good to call a gradient 2:1 because the graph might be a plot of temperature per unit time or rise in current plotted against rise in voltge.Where would you be if in practise you had a graph of a straight line where the change in x and the corresponding y was 213 :99,you would have to give the result 0.465 for the slope..In the last part of your question you should understand it simply as "when x is increased by 1 unit the y value will change by 17 in other words a steep gradient of tangent = 17 which gives an angle of slope 86.633.....degrees anticlockwise from the horizontal. In other words when x changes by 1 unit y changes by 17 units.The confusion will soon disappear.Be careful about statements about run/rise.Run sometimes is taken to mean the length of the hypotenuse which of course would be the measure of how far a car runs as it covers a given VERTICAL distance on a slope.