Use a graphing calculator to graph each equation in the standard viewing window. -2x + 5y = 10

Verified step by step guidance

1. Rewrite the equation in slope-intercept form (y = mx + b) by solving for y. Start with the equation: \(-2x + 5y = 10\).
2. Add \(2x\) to both sides to isolate the term with y: \(5y = 2x + 10\).
3. Divide every term by 5 to solve for y: \(y = \frac{2}{5}x + 2\).
4. Identify the slope (m) and y-intercept (b) from the equation \(y = \frac{2}{5}x + 2\). Here, the slope m is \(\frac{2}{5}\) and the y-intercept b is 2.
5. Use a graphing calculator to plot the line using the slope and y-intercept. Start at the y-intercept (0, 2) and use the slope \(\frac{2}{5}\) to find another point by rising 2 units and running 5 units to the right.

Key Concepts

Standard Form of a Linear Equation

The standard form of a linear equation is typically expressed as Ax + By = C, where A, B, and C are constants. This format allows for easy identification of the coefficients and intercepts, which are essential for graphing. In the given equation, -2x + 5y = 10, the coefficients can be used to determine the slope and y-intercept, facilitating the graphing process.

Graphing Calculators

Graphing calculators are powerful tools that allow users to visualize mathematical functions and equations. They can plot graphs based on input equations, providing a visual representation of relationships between variables. Understanding how to input equations and adjust viewing windows is crucial for effectively using these devices to analyze linear equations like the one provided.

Viewing Window

The viewing window on a graphing calculator defines the range of x and y values displayed on the graph. Setting an appropriate viewing window is essential to ensure that the graph is fully visible and accurately represents the equation. For the equation -2x + 5y = 10, selecting a window that captures the intercepts and slope will provide a clearer understanding of the line's behavior.