Graph each equation. 2x +5y = 20

Verified step by step guidance

1. Rewrite the given equation \$2x + 5y = 20\( in slope-intercept form \)y = mx + b\( by isolating \)y\(. Start by subtracting \)2x\( from both sides: \)5y = -2x + 20$.
2. Divide every term by 5 to solve for \(y\): \(y = \frac{-2}{5}x + 4\).
3. Identify the slope \(m = -\frac{2}{5}\) and the y-intercept \(b = 4\). This means the graph crosses the y-axis at the point \((0, 4)\).
4. Plot the y-intercept point \((0, 4)\) on the coordinate plane.
5. Use the slope \(-\frac{2}{5}\) to find another point: from \((0, 4)\), move down 2 units and right 5 units, then plot this second point. Draw a straight line through these two 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 forming a line.

Slope-Intercept Form

Rearranging the equation into slope-intercept form (y = mx + b) helps identify the slope (m) and y-intercept (b). This form makes graphing easier by showing how the line rises or falls and where it crosses the y-axis.

Plotting Points and Intercepts

Finding intercepts by setting x=0 to find y-intercept and y=0 to find x-intercept provides key points to plot. Plotting these points and drawing a line through them accurately represents the graph of the equation.