To graph a linear equation in gradient-intercept form (y = mx + b), you first locate the y-intercept, then use the gradient (slope) to find additional points and draw the line.
Here's a step-by-step breakdown:
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Identify the y-intercept: In the equation y = mx + b, the y-intercept is represented by 'b'. This is the point where the line crosses the y-axis, and its coordinates are (0, b). Plot this point on the coordinate plane.
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Identify the gradient (slope): The gradient is represented by 'm' in the equation y = mx + b. It describes the steepness and direction of the line. The gradient can be interpreted as "rise over run."
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Use the gradient to find a second point: Starting from the y-intercept, use the gradient to find another point on the line.
- If the gradient is a whole number (e.g., 2), rewrite it as a fraction over 1 (e.g., 2/1). This means for every 1 unit you move to the right (run), you move 2 units up (rise).
- If the gradient is a fraction (e.g., 1/2), move 2 units to the right (run) and 1 unit up (rise).
- If the gradient is negative (e.g., -1/3), move 3 units to the right (run) and 1 unit down (rise).
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Draw the line: Once you have two points (the y-intercept and the point you found using the gradient), use a ruler or straightedge to draw a straight line through these two points. Extend the line beyond the two points to represent the infinite nature of the linear equation.
Example:
Let's graph the equation y = 2x + 1.
- Y-intercept: The y-intercept is 1, so plot the point (0, 1).
- Gradient: The gradient is 2, which can be written as 2/1.
- Second point: Starting from (0, 1), move 1 unit to the right and 2 units up. This gives you the point (1, 3).
- Draw the line: Draw a straight line through the points (0, 1) and (1, 3).
