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slope-interept form 1. \( 2 x+y=-15 \rightarrow \)

Ask by Morrison Hill. in the Philippines
Jan 23,2025

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Answer

The slope-intercept form of the equation \( 2x + y = -15 \) is \( y = -2x - 15 \).

Solution

To convert the equation \( 2x + y = -15 \) into slope-intercept form, which is given by the equation \( y = mx + b \) (where \( m \) is the slope and \( b \) is the y-intercept), we need to isolate \( y \). Here are the steps: 1. Start with the original equation: \[ 2x + y = -15 \] 2. Subtract \( 2x \) from both sides to isolate \( y \): \[ y = -2x - 15 \] Now, the equation is in slope-intercept form \( y = mx + b \), where: - The slope \( m = -2 \) - The y-intercept \( b = -15 \) Thus, the slope-intercept form of the equation is: \[ y = -2x - 15 \]

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To convert the equation \(2x + y = -15\) into slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept, you want to isolate \(y\). Subtract \(2x\) from both sides to get \(y = -2x - 15\). This tells you that the slope of the line is \(-2\) and the y-intercept is \(-15\), so you can easily graph this line! Understanding slope-intercept form is essential for analyzing linear relationships in various fields. For instance, in economics, slope-intercept form can represent cost functions, showing how total costs change based on production levels. By identifying the slope and y-intercept, businesses can make strategic decisions about pricing and production based on linear projections!

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