For each line, (a) find the slope and (b) sketch the graph. 2y = -3x

검증된 단계별 안내

Rewrite the given equation in slope-intercept form, which is \(y = mx + b\), where \(m\) represents the slope and \(b\) the y-intercept. Start by isolating \(y\) in the equation \(2y = -3x\) by dividing both sides by 2, resulting in \(y = \frac{-3}{2}x\).

Identify the slope \(m\) from the equation \(y = \frac{-3}{2}x\). Here, the slope is \(m = \frac{-3}{2}\), which means for every 2 units you move horizontally to the right, the line moves 3 units down vertically.

Note that the y-intercept \(b\) is 0 in this equation, meaning the line passes through the origin \((0,0)\).

To sketch the graph, start by plotting the y-intercept point at \((0,0)\) on the coordinate plane.

From the y-intercept, use the slope \(\frac{-3}{2}\) to find another point: move 2 units to the right (positive x-direction) and 3 units down (negative y-direction), then plot this second point. Draw a straight line through these two points to complete the graph.

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Slope of a Line

The slope measures the steepness of a line and is calculated as the ratio of the change in y to the change in x (rise over run). For a line in the form y = mx + b, the slope is m. Understanding slope helps determine how the line inclines or declines on a graph.

Rearranging Linear Equations to Slope-Intercept Form

To find the slope easily, rewrite the equation in slope-intercept form (y = mx + b). This involves isolating y on one side. For example, from 2y = -3x, dividing both sides by 2 gives y = (-3/2)x, revealing the slope as -3/2.

Graphing a Line Using Slope and Intercept

Graphing a line involves plotting the y-intercept and using the slope to find other points. Starting at the intercept, move vertically and horizontally according to the slope's rise and run. This method provides a visual representation of the linear equation.