Questions: Graph the line. y=2x-7

Graph the line. y=2x-7
Transcript text: Graph the line. \[ y=2 x-7 \]
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Solution

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Solution Steps

Step 1: Identify the Slope and Y-Intercept

The given equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. For the equation \( y = 2x - 7 \):

  • Slope (\( m \)) = 2
  • Y-intercept (\( b \)) = -7
Step 2: 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 \( y = 2x - 7 \), the y-intercept is -7. Plot the point (0, -7) on the graph.

Step 3: Use the Slope to Find Another Point

The slope of 2 means that for every 1 unit increase in \( x \), \( y \) increases by 2 units. Starting from the y-intercept (0, -7):

  • Move 1 unit to the right (x = 1)
  • Move 2 units up (y = -7 + 2 = -5) Plot the point (1, -5) on the graph.
Step 4: Draw the Line

Draw a straight line through the points (0, -7) and (1, -5). This line represents the equation \( y = 2x - 7 \).

Final Answer

The graph of the line \( y = 2x - 7 \) is a straight line passing through the points (0, -7) and (1, -5).

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