Graphing Equations and Linear Functions
This page introduces fundamental concepts in graphing equations and working with linear functions.
The first exercise demonstrates how to graph an equation given specific points. This skill is crucial for visualizing mathematical relationships.
Example: A graph is shown with points 2,3 and −2,1, illustrating how to plot points on a coordinate system.
Next, the page covers how to determine the equation of a line given two points. This process involves calculating the slope and y-intercept of the line.
Highlight: The equation of a line is given in the form y = ax + b, where 'a' is the slope and 'b' is the y-intercept.
The method for finding the slope a and y-intercept b is clearly outlined:
- Calculate the slope using the formula: a = y2−y1 / x2−x1
- Use one of the given points to solve for the y-intercept b
Example: Using points A−3,5 and B1,13, the slope is calculated as a = 13−5 / 1−(−3) = 2, and the y-intercept is determined to be b = 11.
The page also covers how to calculate a rate of change, which is a crucial concept in various fields, including economics.
Example: The price of apricots changes from €2.50 to €1.80 per kg. The rate of change is calculated as 1.80−2.50 / 2.50 = -28%.
Lastly, the page demonstrates how to determine images of a function for given x-values, which is essential for understanding function behavior.
Vocabulary: The 'image' of a value is the y-coordinate that corresponds to a given x-coordinate on a function.