Grade 9 MATH Term 1 Week 4: Slopes and Zeros of Linear Functions | MATATAG First Term/Q1 Tagalog

The video introduces linear functions as those whose graphs are straight lines, have a constant rate of change, and a degree of 1 or less in their equation. It uses an example of Mika's spending to illustrate these concepts, showing how a constant change in money spent daily relates to a linear function. Exercises are provided to help differentiate linear from non-linear functions based on tables, graphs, and equations.

Slope describes the steepness of a line and is the ratio of vertical change (rise) to horizontal change (run), denoted by 'M'. The video reviews how to calculate slope from a graph by counting units, and from two given points using the formula M = (y2 - y1) / (x2 - x1). It also covers different types of slopes: positive, negative, zero, and undefined.

The zero of a function is the value of x that makes the output (f(x) or y) equal to zero. It's also defined as the x-value where the line crosses the x-axis on a graph. The video clarifies that the zero is the x-value, not the coordinate point itself (which is the x-intercept).

This section explains how to find the slope and zero when a linear function is represented by a graph. For the slope, two integer points on the line are chosen, and the rise over run is calculated. For the zero, the point where the line intersects the x-axis is identified, and its x-coordinate is the zero.

The video demonstrates how to find the slope and zero from a linear function's equation, particularly when it's in the y = mx + b (slope-intercept) form. 'M' directly gives the slope. To find the zero, the function (f(x) or y) is set to zero, and the equation is solved for x. Examples include rearranging equations from standard form to slope-intercept form before identifying the slope and zero.

This part focuses on calculating the slope and zero from a table of values. The slope is found by determining the constant change in output (y) over the constant change in input (x). To find the zero, one looks for the x-value where the corresponding output (f(x) or y) is zero. If not directly present, the slope formula can be used with two points from the table, followed by solving for the zero using the derived slope-intercept form.

The video concludes with a series of activities for viewers to practice determining slopes and zeros from graphs, equations, and tables, encouraging them to test their understanding. It offers a way to check answers with teachers who have access to the provided answer keys.