To graph the line given by the equation \( y = 7x + 2 \), we can use the slope-intercept form of a linear equation, which is \( y = mx + b \), where:
- \( m \) is the slope of the line,
- \( b \) is the y-intercept.
From the equation \( y = 7x + 2 \):
- The slope \( m \) is 7.
- The y-intercept \( b \) is 2.
Steps to graph the line:
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Plot the y-intercept: Start by plotting the y-intercept on the graph. Since \( b = 2 \), you will place a point at (0, 2) on the y-axis.
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Use the slope to find another point: The slope of 7 can be expressed as \( \frac{7}{1} \). This means that for every 7 units you move up in the y-direction, you move 1 unit to the right in the x-direction.
- Starting from the y-intercept (0, 2):
- Move 1 unit to the right (to \( x = 1 \)).
- Move up 7 units (from \( y = 2 \) to \( y = 9 \)).
- This gives you the point (1, 9).
- Starting from the y-intercept (0, 2):
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Draw the line: Connect the two points (0, 2) and (1, 9) with a straight line. Extend the line in both directions, and use arrows to indicate that it continues indefinitely.
Summary of points to plot:
- (0, 2) (y-intercept)
- (1, 9) (using the slope)
Final result:
You should have a straight line that passes through the points (0, 2) and (1, 9) with a steep upward slope.
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