Questions: Graph the linear equation. x-3y=-6

Graph the linear equation. x-3y=-6
Transcript text: Graph the linear equation. \[ x-3 y=-6 \]
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Solution

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Solution Steps

Step 1: Identify the equation to be graphed

The given equation is \( y = 3x - 8 \).

Step 2: Determine the slope and y-intercept

The equation \( y = 3x - 8 \) is in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

  • Slope (\( m \)) = 3
  • Y-intercept (\( b \)) = -8
Step 3: Plot the y-intercept

Locate the y-intercept on the graph. The y-intercept is the point where the line crosses the y-axis. For \( y = 3x - 8 \), the y-intercept is -8. Plot the point (0, -8) on the graph.

Step 4: Use the slope to find another point

The slope of 3 means that for every 1 unit increase in \( x \), \( y \) increases by 3 units. Starting from the y-intercept (0, -8):

  • Move 1 unit to the right (x = 1)
  • Move 3 units up (y = -8 + 3 = -5) Plot the point (1, -5).
Step 5: Draw the line

Draw a straight line through the points (0, -8) and (1, -5).

Final Answer

The graph of the equation \( y = 3x - 8 \) is a straight line passing through the points (0, -8) and (1, -5).

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