Slope-intercept form: graph an equation

Key Notes:

Definition

The slope-intercept form of a linear equation is:

y = mx + b

Where:

• m = slope of the line (rise over run)
• b = y-intercept (the point where the line crosses the y-axis)

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Understanding the Slope (m)

• Slope = change in y / change in x = rise / run
• Positive slope → line rises from left to right
• Negative slope → line falls from left to right
• Zero slope → horizontal line
• Undefined slope → vertical line (not in slope-intercept form)

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Understanding the Y-intercept (b)

• Point where the line crosses the y-axis
• Coordinates are always (0,b)

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Steps to Graph an Equation in Slope-Intercept Form

• Identify the slope (m) and y-intercept (b) from the equation.
• Plot the y-intercept on the y-axis.
• Use the slope to find another point:
  • From the y-intercept, move rise units up/down and run units right.
• Draw the straight line through the points.
• Extend the line and label it.

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Example

Equation: y = 2x − 3

• m = 2 → rise = 2, run = 1
• b = -3 → y-intercept = (0, -3)

Graphing:

• Plot (0, -3)
• From (0, -3), go up 2 and right 1 → (1, -1)
• Draw line through the points.

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Key Points to Remember

• Slope is a measure of steepness.
• Y-intercept tells where the line starts on the y-axis.
• Only two points are needed to draw a line, but more points can make it accurate.
• Always check if the equation is in y = mx + b form; if not, rearrange it.