Chapter Five - Algebra

Big Ideas

Lesson 1 Linear Functions

• Linear functions describe numerous real-world situations that involve constant rates of change (slope), such as cost, distance, and speed.

• In a linear function, a constant change in x corresponds to a constant change in y.

• The STANDARD FORM of a linear equation is Ax + By = C.

• The graph of a linear function is a line.

Lessons 2,3,4 - Slope and Intercepts

• SLOPE is the constant rate of change shown by a line.

• SLOPE = change in y / change in x = y2 – y1 / x2 – x1

The x-intercept is the x-coordinate of the point where the graph crosses the x-axis (where y = 0).

The y-intercept is the y-coordinate of the point where the graph crosses the y-axis (where x = 0).

Lesson 5 Direct Variation

• Many real-world relationships involve direct variations, including relationships in science, cooking, and medicine.

• When the dependent variable y depends only on the value of the independent variable x, the linear relationship is a direct variation, written in the form y = kx, where k is the constant of variation. (Direct variation contains only multiplication and always has a y-intercept of 0).

Lessons 6 and 7 – Forms of Linear Equations

• Linear equations can be written in Slope-Intercept Form, Point-Slope Form, or Standard Form.

Lesson 8 Slopes of Parallel and Perpendicular Lines

• Parallel lines have the same slope. • The slopes of perpendicular lines have a

product of -1.

Lesson 9 Transforming Linear Functions

• For the function f(x) = mx + b (also known as y = mx + b):

• A change in b (the y-intercept) results in a translation (slide).

• A change in m (the slope) results in a rotation (turn).

• Multiplying m (the slope) by -1 results in a reflection (flip) across the y axis.