Question
\( 1 \leftarrow \left\lvert\, \begin{array}{c}\text { Find the slope of the line. } \\ y=-3 x+4\end{array}\right. \)
Ask by Hilton Parry. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The slope of the line \( y = -3x + 4 \) is \( -3 \).
Solution
To find the slope of the line given by the equation \( y = -3x + 4 \), we can follow these steps:
1. **Identify the form of the equation**: The equation is in the slope-intercept form, which is given by \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
2. **Extract the slope**: In the equation \( y = -3x + 4 \), the coefficient of \( x \) is \( -3 \). This coefficient represents the slope of the line.
Thus, the slope of the line is:
\[
m = -3
\]
Therefore, the slope of the line \( y = -3x + 4 \) is \( -3 \).
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Simplify this solution The Deep Dive
The slope of a line in the slope-intercept form \(y = mx + b\) is represented by the coefficient of \(x\). In your equation \(y = -3x + 4\), the coefficient of \(x\) is \(-3\). This means the slope of the line is \(-3\), indicating that for every unit increase in \(x\), \(y\) decreases by 3 units! Additionally, understanding the slope isn’t just about numbers—it tells you about the direction and steepness of the line. A negative slope like \(-3\) means the line declines as you move from left to right. If you visualize this on a graph, you’ll see a nice downward slant!
