Graph each equation. 2x +5y = 20

Verified step by step guidance

1. Rewrite the given equation in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Start with the equation: \$2x + 5y = 20$.
2. Isolate the \(y\) term by subtracting \$2x\( from both sides: \)5y = -2x + 20$.
3. Divide every term by 5 to solve for \(y\): \(y = \frac{-2}{5}x + 4\).
4. Identify the slope and y-intercept from the equation \(y = -\frac{2}{5}x + 4\). The slope \(m\) is \(-\frac{2}{5}\) and the y-intercept \(b\) is 4.
5. Plot the y-intercept point \((0, 4)\) on the graph. Then use the slope \(-\frac{2}{5}\) to find another point by moving down 2 units and right 5 units from the y-intercept. Draw a straight line through these points to graph the equation.

Key Concepts

Linear Equations in Two Variables

A linear equation in two variables, like 2x + 5y = 20, represents a straight line on the coordinate plane. Each solution (x, y) satisfies the equation, and the graph is the set of all such points.

Slope-Intercept Form

Rearranging the equation into slope-intercept form (y = mx + b) helps identify the slope (m) and y-intercept (b), making it easier to graph the line by starting at the intercept and using the slope to find other points.

Plotting Points and Drawing the Graph

To graph the equation, find at least two points that satisfy it by choosing values for x or y, plot these points on the coordinate plane, and draw a straight line through them to represent all solutions.