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

검증된 단계별 안내

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.

Compare the given equation \(y = -2x + 7\) to the slope-intercept form to determine the values of \(m\) and \(b\).

From the equation, observe that the coefficient of \(x\) is \(-2\), so the slope \(m\) is \(-2\).

Also, the constant term is \(7\), which means the y-intercept \(b\) is \(7\).

Therefore, the slope is \(-2\) and the y-intercept is \(7\).

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주요 개념

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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.

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