Questions: Find the slope and y-intercept of the line. f(x)=-4x+15

Find the slope and y-intercept of the line. f(x)=-4x+15
Transcript text: Find the slope and $y$-intercept of the line. \[ f(x)=-4 x+15 \]
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Solution

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Solution Steps

To find the slope and y-intercept of the line given by the equation \( f(x) = -4x + 15 \), we can identify the slope and y-intercept directly from the equation. The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Solution Approach
  1. Identify the slope \( m \) from the equation \( f(x) = -4x + 15 \).
  2. Identify the y-intercept \( b \) from the equation \( f(x) = -4x + 15 \).
Step 1: Identify the Slope

The given equation of the line is \( f(x) = -4x + 15 \). In the slope-intercept form \( y = mx + b \), the coefficient of \( x \) represents the slope \( m \). Therefore, the slope of the line is: \[ m = -4 \]

Step 2: Identify the Y-Intercept

In the same equation \( f(x) = -4x + 15 \), the constant term represents the y-intercept \( b \). Thus, the y-intercept of the line is: \[ b = 15 \]

Final Answer

The slope of the line is \( \boxed{-4} \) and the y-intercept is \( \boxed{15} \).

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