Give the slope and y-intercept of each line whose equation is given. Then graph the linear function. y = -2x/5+6

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Identify the given linear equation: \(y = -\frac{2x}{5} + 6\).

Rewrite the equation in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Here, the equation is already in this form with \(m = -\frac{2}{5}\) and \(b = 6\).

Determine the slope \(m = -\frac{2}{5}\), which means the line falls 2 units vertically for every 5 units it moves horizontally to the right.

Identify the y-intercept \(b = 6\), which is the point where the line crosses the y-axis, at \((0, 6)\).

To graph the line, start by plotting the y-intercept \((0, 6)\) on the coordinate plane, then use the slope to find another point by moving 5 units to the right and 2 units down, and draw the line through these points.

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주요 개념

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Slope of a Linear Function

The slope represents the rate of change of the function and indicates how steep the line is. It is the coefficient of x in the equation y = mx + b, where m is the slope. A negative slope means the line decreases as x increases.

Y-Intercept of a Linear Function

The y-intercept is the point where the line crosses the y-axis, given by the constant term b in y = mx + b. It shows the value of y when x is zero and helps in graphing the line accurately.

Graphing Linear Functions

Graphing involves plotting the y-intercept on the coordinate plane and using the slope to find other points by rising and running from the intercept. Connecting these points forms the line representing the function.