Find the slope and y-intercept of each line, and graph it. x+2y = -4

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Rewrite the given equation \( x + 2y = -4 \) in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

To isolate \( y \), subtract \( x \) from both sides: \( 2y = -x - 4 \).

Next, divide every term by 2 to solve for \( y \): \( y = \frac{-x}{2} - 2 \).

Identify the slope \( m \) as the coefficient of \( x \), which is \( -\frac{1}{2} \), and the y-intercept \( b \) as the constant term, which is \( -2 \).

To graph the line, plot the y-intercept point \( (0, -2) \) on the coordinate plane, then use the slope \( -\frac{1}{2} \) to find another point by moving down 1 unit and right 2 units from the y-intercept, and draw the line through these points.

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주요 개념

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Slope-Intercept Form of a Line

The slope-intercept form is y = mx + b, where m represents the slope and b the y-intercept. Converting an equation into this form makes it easier to identify these values directly and to graph the line.

Slope of a Line

The slope measures the steepness and direction of a line, calculated as the ratio of the change in y to the change in x (rise over run). A positive slope rises to the right, while a negative slope falls.

Y-Intercept

The y-intercept is the point where the line crosses the y-axis, occurring when x = 0. It represents the value of y at this point and is essential for graphing the line accurately.