Let's break down the equation and find the points needed to graph \( y = -5x + 5 \).
Step 1: Find the y-intercept
The y-intercept of a linear equation in the form \( y = mx + b \) occurs when \( x = 0 \).
Substituting \( x = 0 \) into the equation:
\[ y = -5(0) + 5 = 5 \]
So the y-intercept is the point \( (0, 5) \).
Step 2: Plot a 2nd point
To plot a second point, we can use the slope of the line. The slope \( m \) in this equation is -5, which can be interpreted as:
- Go down 5 (since it's negative)
- Go right 1
Starting from the initial point \( (0, 5) \):
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From \( (0, 5) \), go down 5 units: \[ 5 - 5 = 0 \quad \Rightarrow \quad y \text{ coordinate is now } 0 \]
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Then, go right 1 unit from \( x = 0 \): \[ 0 + 1 = 1 \quad \Rightarrow \quad x \text{ coordinate is now } 1 \]
Thus, the second point is \( (1, 0) \).
Summary of points:
- The initial point (y-intercept) is \( (0, 5) \).
- The second point calculated is \( (1, 0) \).
You can now plot these points to graph the line for the equation \( y = -5x + 5 \).