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

Verified step by step guidance

1. Identify the slope-intercept form of a linear equation, which is given by \(y = mx + b\), where \(m\) represents the slope and \(b\) represents the y-intercept.
2. Compare the given equation \(y = -2x + 7\) to the slope-intercept form to determine the values of \(m\) and \(b\).
3. From the equation, observe that the coefficient of \(x\) is \(-2\), so the slope \(m\) is \(-2\).
4. Also, the constant term is \$7\(, which means the y-intercept \)b\( is \)7$.
5. Therefore, the slope is \(-2\) and the y-intercept is \$7$.

Key Concepts

Slope of a Line

The slope of a line measures its steepness and direction, represented by the coefficient of x in the equation y = mx + b. It indicates how much y changes for a unit change in x. A negative slope means the line decreases as x increases.

Y-Intercept of a Line

The y-intercept is the point where the line crosses the y-axis, given by the constant term b in the equation y = mx + b. It represents the value of y when x is zero, providing a starting point for graphing the line.

Slope-Intercept Form of a Linear Equation

The slope-intercept form y = mx + b expresses a linear equation clearly showing the slope (m) and y-intercept (b). This form makes it easy to identify key features of the line and to graph it quickly.