Fill in the blank(s) to correctly complete each sentence. The graph of the line y= -2x+7 has slope ______ and y-intercept ______.

Key Concepts

Slope

The slope of a line in a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). In the equation y = mx + b, 'm' denotes the slope. A positive slope indicates that as x increases, y also increases, while a negative slope indicates that y decreases as x increases. For the equation y = -2x + 7, the slope is -2.

Y-Intercept

The y-intercept of a line is the point where the line crosses the y-axis, which occurs when x equals zero. In the slope-intercept form of a linear equation, y = mx + b, 'b' represents the y-intercept. This value indicates the starting point of the line on the y-axis. For the equation y = -2x + 7, the y-intercept is 7, meaning the line crosses the y-axis at the point (0, 7).

Linear Equation

A linear equation is an algebraic equation that represents a straight line when graphed on a coordinate plane. It is typically expressed in the form y = mx + b, where 'm' is the slope and 'b' is the y-intercept. Linear equations can model relationships with constant rates of change, making them fundamental in algebra. The equation y = -2x + 7 is a specific example of a linear equation.