Fill in the blank to correctly complete each sentence. The y-intercept of the graph of y = -2x + 6 is ________.

Verified step by step guidance

1. Identify the y-intercept in the equation of the line, which is in the form y = mx + b, where b is the y-intercept.
2. In the given equation y = -2x + 6, compare it with the standard form y = mx + b.
3. Notice that the term +6 corresponds to the b in the standard form.
4. The y-intercept is the value of y when x is 0, which is represented by the constant term in the equation.
5. Therefore, the y-intercept of the graph of y = -2x + 6 is the constant term, which is 6.

Key Concepts

Linear Equations

A linear equation is an algebraic expression that represents a straight line when graphed on a coordinate plane. It is typically written in the form y = mx + b, where m is the slope and b is the y-intercept. Understanding this form is crucial for identifying key features of the graph, such as where it intersects the y-axis.

Y-Intercept

The y-intercept of a linear equation is the point where the graph crosses the y-axis. This occurs when the value of x is zero. In the equation y = -2x + 6, the y-intercept can be found by substituting x = 0, which simplifies the equation to y = 6, indicating that the graph intersects the y-axis at the point (0, 6).

Graphing Linear Functions

Graphing linear functions involves plotting points that satisfy the equation and connecting them to form a straight line. The slope indicates the direction and steepness of the line, while the y-intercept provides a starting point on the graph. Mastery of graphing techniques is essential for visualizing relationships between variables in linear equations.