Use a graphing calculator to graph each equation in the standard viewing window. 3x + 4y = 6

Verified step by step guidance

1. Rewrite the equation in slope-intercept form $y=mx+b$. Start by isolating $y$ on one side of the equation.
2. Subtract $3x$ from both sides to get $4y=-3x+6$.
3. Divide every term by 4 to solve for $y$, resulting in $y=-\frac{3}{4}x+\frac{3}{2}$.
4. Identify the slope $m=-\frac{3}{4}$ and the y-intercept $b=\frac{3}{2}$.
5. Use a graphing calculator to plot the line using the slope and y-intercept, ensuring the graph is displayed in the standard viewing window.

Key Concepts

Standard Form of a Linear Equation

The standard form of a linear equation is expressed as Ax + By = C, where A, B, and C are constants. In this format, the coefficients of x and y provide a clear way to identify the slope and intercepts of the line. For the equation 3x + 4y = 6, it can be rearranged to find the y-intercept and slope, which are essential for graphing.

Graphing Linear Equations

Graphing linear equations involves plotting points that satisfy the equation on a coordinate plane. The line formed by connecting these points represents all solutions to the equation. Understanding how to find key points, such as intercepts, helps in accurately sketching the graph, especially when using a graphing calculator.

Graphing Calculator Functions

A graphing calculator is a powerful tool that allows users to visualize equations and functions. It can plot graphs in real-time, providing a standard viewing window that typically ranges from -10 to 10 on both axes. Familiarity with the calculator's functions, such as inputting equations and adjusting viewing windows, is crucial for effectively graphing and analyzing linear equations.