Change the equation of the line (indicated by the LINE...

Change the equation of the line (indicated by the LINE EQUATION comment in the previous code) to the following: $$ y=\operatorname{int}(0.05 * x)-100 $$ The value of 100 at the end is the $y$ intercept and as such (because the $y$ axis is flipped), the line will cross the $y$ axis further up the screen. But what of int $(0.05 * x)$ ? Well, 0.05 is the slope, which in this case is very flat. The typecast to an integer by wrapping the value with brackets and typing int at the front are to appease the set_at ( ) method. Why? Well, let's consider something. The window is 1,000 pixels wide by 800 pixels high. If you wanted to plot a point at pixel $(10,10)$, I'm sure you can determine where that would appear. However, what if you wanted to plot a point at $(10.5,10)$ ?

Change the equation of the line (indicated by the LINE EQUATION comment in the previous code) to the following:
$$
y=\operatorname{int}(0.05 * x)-100
$$

The value of 100 at the end is the $y$ intercept and as such (because the $y$ axis is flipped), the line will cross the $y$ axis further up the screen.
But what of int $(0.05 * x)$ ? Well, 0.05 is the slope, which in this case is very flat. The typecast to an integer by wrapping the value with brackets and typing int at the front are to appease the set_at ( ) method. Why? Well, let's consider something. The window is 1,000 pixels wide by 800 pixels high. If you wanted to plot a point at pixel $(10,10)$, I'm sure you can determine where that would appear. However, what if you wanted to plot a point at $(10.5,10)$ ?

Key Concepts

Discrete Pixel Coordinates

In computer graphics, the display is composed of a finite number of pixels, meaning positions must be represented as integers. This discrete nature of pixels necessitates adjustments like typecasting when calculations result in floating-point numbers, ensuring that graphical operations align with the grid of pixels on the screen.

Typecasting to Integer

Typecasting, such as converting a floating-point number to an integer, is a process used in programming to change a value from one data type to another. In the context of pixel coordinates, it's necessary because screen pixels are discrete units and require integer values to specify exact positions.

Slope

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is; a small slope means a nearly horizontal line, while a larger slope implies a steeper line. Understanding the slope is critical for correctly scaling and positioning lines in graphical representations.

Line Equation

A line equation, generally written as y = mx + b, describes the relationship between the x and y coordinates in a two-dimensional space by using a constant slope (m) and a y-intercept (b). This formulation is fundamental in both mathematics and computer graphics to define linear relationships and to draw straight lines on a display.

Y-Intercept

The y-intercept is the point where the line crosses the y-axis, corresponding to the value of y when x is zero. In computer graphics, particularly when the y-axis is flipped, the y-intercept plays a crucial role in determining where on the screen the line will start or cross the vertical axis.

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