91Ó°ÊÓ

Graphing linear functions involves transforming an equation into a visual line on a graph. The equation given, \( s = 7 - 2t \), is a classic example. Here, the function expresses a relationship where the value of \( s \) depends on \( t \). When graphing such a function, start by identifying two crucial components: the slope and the y-intercept.

• **Y-intercept**: This is the point where the graph crosses the y-axis. For our equation, the y-intercept is 7.
• **Slope**: This tells us how steep or flat the graph is. It measures the rate of change in \( s \) for each unit change in \( t \). Here, the slope is -2, indicating a downward slope.

Once these are plotted, connect the dots to visualize the straight line representing the linear function. This process helps illustrate how changes in \( t \) affect \( s \) visually. The line should extend infinitely, so follow the slope from both direction from the plotted points to complete the graph.

The slope-intercept form of a linear equation is one of the most common ways to express linear relationships. It's written as \( y = mx + b \), where \( m \) and \( b \) reveal vital information about the line. In \( s = -2t + 7 \), we see it mirrors the form \( y = mx + b \) with:- \( m = -2 \) indicating the slope- \( b = 7 \) indicating the y-intercept.
The **slope** \( m = -2 \) describes how much \( s \) decreases for each increase in \( t \). A negative slope signals a descending line as you move from left to right on the graph.
The **y-intercept** \( b = 7 \) is where \( s \) stands when \( t = 0 \). Visually, it is the starting point on the y-axis. Understanding these two parameters allows one to sketch the line easily. Knowing that you begin at height 7 on the y-axis, the slope tells you to move down two steps vertically for every one step horizontally to the right. This quick movement method provides a reliable way to draw a line accurately.

Every function, including \( s = 7 - 2t \), comprises dependent and independent variables. It's crucial to identify which is which, as it determines the relationship dynamics in the equation.
- **Dependent Variable**: This is the variable that relies on the other. In our function, \( s \) is the dependent variable. It changes responding to the modifications in \( t \).- **Independent Variable**: This is the variable you control or change. In this function, \( t \) serves this role.
If you imagine \( t \) as a time or a condition, you can see how varying it indirectly shapes \( s \). On graphs and in calculations, the independent variable is traditionally plotted on the horizontal axis (x-axis), while the dependent variable appears on the vertical axis (y-axis). Whenever you study or graph linear equations, first determine these variables to comprehend how they interact within the function thoroughly.