Find the slope and y-intercept of each line, and graph it. 4y = -3x

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Rewrite the given equation in slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Start by isolating \(y\) on one side of the equation: \(4y = -3x\).

Divide both sides of the equation by 4 to solve for \(y\): \(y = \frac{-3x}{4}\).

Identify the slope \(m\) and the y-intercept \(b\) from the equation \(y = -\frac{3}{4}x + 0\). Here, the slope \(m\) is \(-\frac{3}{4}\) and the y-intercept \(b\) is 0.

Interpret the y-intercept: since \(b = 0\), the line crosses the y-axis at the origin \((0,0)\).

To graph the line, plot the y-intercept at \((0,0)\), then use the slope \(-\frac{3}{4}\) to find another point by moving down 3 units and right 4 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 of a line is y = mx + b, where m represents the slope and b represents 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 to the right.

Y-Intercept

The y-intercept is the point where the line crosses the y-axis, occurring when x = 0. It is represented by the constant term b in the slope-intercept form and is essential for graphing the line accurately.