Use a graphing calculator to graph each equation in the standard viewing window. y = 3x + 4

Verified step by step guidance

1. Identify the equation given: \(y = 3x + 4\). This is a linear equation in slope-intercept form, where the slope \(m = 3\) and the y-intercept \(b = 4\).
2. Understand that the slope \(3\) means the line rises 3 units vertically for every 1 unit it moves horizontally to the right.
3. The y-intercept \(4\) means the line crosses the y-axis at the point \((0, 4)\).
4. To graph the equation on a graphing calculator, enter the equation \(y = 3x + 4\) into the function input (usually labeled as \(Y_1\)).
5. Use the standard viewing window (typically \(x\) and \(y\) values from \(-10\) to \(10\)) to view the graph, and observe the straight line crossing the y-axis at 4 and rising with slope 3.

Key Concepts

Linear Equations

A linear equation represents a straight line when graphed and has the form y = mx + b, where m is the slope and b is the y-intercept. Understanding this form helps in predicting the shape and position of the graph.

Slope and Y-Intercept

The slope (m) indicates the steepness and direction of the line, while the y-intercept (b) is the point where the line crosses the y-axis. For y = 3x + 4, the slope is 3 and the y-intercept is 4.

Using a Graphing Calculator

A graphing calculator allows you to input equations and view their graphs within a standard window, typically ranging from -10 to 10 on both axes. This tool helps visualize the behavior of functions quickly and accurately.