Find the equation of the straight line with a -intercept of 2 and a
gradient of 12.
Give your answer in the form

To find the equation of a straight line, you can use the slope-intercept form, which is , where represents the gradient (slope) and is the -intercept.

Given that the -intercept is 2 and the gradient is 12, you can substitute these values into the formula:

So, the equation of the line is .

Now, how cool is it that this simple equation describes a line that slopes upward at a steep angle of 12, all while intersecting the -axis at 2? Just imagine plotting it on a graph: as you move right, the line shoots up quickly!

For practical application, such a line could model real-world scenarios, like predicting output levels based on increased input in various fields—be it economics with profits increasing steeply with investment, or in physics, measuring speed versus time where each unit of time significantly elevates the speed.