Graph each equation. 2x +5y = 20

Verified step by step guidance

1. Step 1: The given equation is in the standard form Ax + By = C. We need to convert it into slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
2. Step 2: To convert the equation into slope-intercept form, isolate y. Subtract 2x from both sides to get 5y = -2x + 20.
3. Step 3: Divide every term by 5 to solve for y. This gives y = -2/5x + 4.
4. Step 4: Now that we have the equation in slope-intercept form, we can identify the slope and y-intercept. The slope (m) is -2/5 and the y-intercept (b) is 4.
5. Step 5: To graph the equation, start by plotting the y-intercept (0,4) on the y-axis. Then, from this point, use the slope to find the next point. Since the slope is -2/5, go down 2 units and to the right 5 units. Plot this point and draw a line through the two points. This line represents the graph of the equation.

Key Concepts

Linear Equations

A linear equation is an algebraic expression that represents a straight line when graphed on a coordinate plane. It typically takes the form Ax + By = C, where A, B, and C are constants. The solutions to a linear equation are the points (x, y) that satisfy the equation, and the graph of the equation shows all these solutions.

Slope-Intercept Form

The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope of the line and b represents the y-intercept. This form is particularly useful for quickly identifying the slope and y-intercept, allowing for easier graphing. Converting a standard form equation, like 2x + 5y = 20, into slope-intercept form can simplify the graphing process.

Graphing Linear Equations

Graphing a linear equation involves plotting points that satisfy the equation on a coordinate plane and connecting them to form a straight line. To graph the equation 2x + 5y = 20, one can find the x-intercept and y-intercept or convert it to slope-intercept form. Understanding how to plot these points accurately is essential for visualizing the relationship between the variables.