Slope-intercept form: find the slope and y-intercept

Key Notes:

Definition

The slope-intercept form of a linear equation is:

y = mx + b

Where:

• m → Slope (rate of change)
• b → Y-intercept (where the line crosses the y-axis)

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Understanding the Slope (m)

• The slope tells how steep the line is and the direction it goes.
• Formula to find slope between two points (x1,y1) and (x2,y2):

m = y2 − y1 / x2 − x1

• Positive slope → line rises from left to right
• Negative slope → line falls from left to right
• Zero slope → horizontal line
• Undefined slope → vertical line (cannot be written in slope-intercept form)

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Understanding the Y-Intercept (b)

• The y-intercept is the point where the line meets the y-axis.
• At the y-intercept, x = 0.
• To find bbb, substitute x = 0 into the equation.

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Steps to Find the Slope and Y-Intercept from an Equation

Case 1: Equation is already in slope-intercept form y = mx + b

• Slope = m (coefficient of xxx)
• Y-intercept = b

Example: y = 2x + 3

• Slope m=2
• Y-intercept b=3 → Point (0, 3)

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Case 2: Equation is in standard form A_x + B_y = C

• Rearrange into y = mx + b by isolating y.

Example: 2x + 3y = 6

1. Subtract 2x : 3y = −2x + 6
2. Divide by 3: y = −2/3 x + 2

• Slope m =−2/3
• Y-intercept b =2 → Point (0, 2)

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Graphing Using Slope and Y-Intercept

1. Plot the y-intercept (0,b) on the graph.
2. Use the slope m = rise/runm to find another point.
3. Draw the line through the points.

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Quick Tips

• Always check if the equation is in y = mx + b form first.
• Slope is change in y / change in x.
• The y-intercept is just the constant term in slope-intercept form.
• A line can be drawn with just mmm and bbb.

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✅ Example Practice

• y = −3x + 4 → m = −3, b = 4
• 5x − y = 10 → Rewrite: y = 5x − 10 → m = 5, b = −10