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To graph the line given by the equation \( y = -5x + 8 \), let’s go through the steps:

1. **Identify the slope and y-intercept**:
   - The equation is in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
   - Here, \( m = -5 \) and \( b = 8 \).

2. **Plot the y-intercept**:
   - The y-intercept is \( 8 \), so place a point at \( (0, 8) \) on the y-axis.

3. **Use the slope to find another point**:
   - The slope \( -5 \) can be interpreted as \( -5/1 \), meaning that for every 1 unit moved to the right (positive x-direction), we move 5 units down (negative y-direction).
   - Starting from \( (0, 8) \), move 1 unit to the right to \( x = 1 \), then move 5 units down to \( y = 3 \). Place another point at \( (1, 3) \).

4. **Draw the line**:
   - Connect the points \( (0, 8) \) and \( (1, 3) \) with a straight line, extending it in both directions.

This line represents the equation \( y = -5x + 8 \) on the graph.

Would you like further details on graphing lines or the reasoning behind each step?

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**Here are some related questions you might find helpful:**

1. How do you graph lines with positive slopes?
2. What is the general form of a line, and how is it different from the slope-intercept form?
3. How would the graph change if the slope were less steep, like \( y = -2x + 8 \)?
4. How do you graph a line given in standard form, such as \( Ax + By = C \)?
5. What is the effect of changing the y-intercept in a linear equation?

**Tip:** When working with a slope, remember that a negative slope means the line goes downward from left to right.

Learn how to graph the line given by the equation y = -5x + 8 using slope-intercept form. This guide covers essential algebra concepts, including identifying the slope and y-intercept, plotting points, and drawing the line. Perfect for students in Grades 8-10.

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