Slope-intercept form is the most common form of linear equations. It clearly shows the slope and y-intercept.
⚠For vertical lines (undefined slope), use x = constant form instead.
What is Slope-Intercept Form?
The slope-intercept form y = mx + b is a way to represent a straight line where m is the slope (rate of change) and b is the y-intercept (where the line crosses the y-axis).
Slope (m)
Rise over run. m = Δy/Δx = (y₂-y₁)/(x₂-x₁). Positive slope = line goes up, negative = goes down.
Y-Intercept (b)
Point where line crosses y-axis (x=0). Found by plugging a point into y = mx + b and solving for b.
Positive Slope
m > 0: Line rises from left to right (y increases as x increases)
Negative Slope
m < 0: Line falls from left to right (y decreases as x increases)
💡 Example: Points (1,3) and (3,7). m=(7-3)/(3-1)=2. b=3-2×1=1. Equation: y = 2x + 1.
Applications
GraphingAlgebraPhysicsEconomicsEngineering
Frequently Asked Questions
What is slope-intercept form?▼
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. This form clearly shows how y changes with x and where the line crosses the y-axis.
How to find slope from two points?▼
Slope m = (y₂ - y₁) / (x₂ - x₁). It represents the rise over run - change in y divided by change in x between two points.
What does the y-intercept represent?▼
The y-intercept (b) is the point where the line crosses the y-axis (when x=0). It represents the starting value of y when x is zero.
When to use slope-intercept form?▼
Use slope-intercept form when you need to quickly identify the slope and y-intercept. It is ideal for graphing lines and making predictions.
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