Work with the equation y = mx + b
Step 1: Identify What You Know
Determine if you have slope (m) and y-intercept (b), or slope (m) and a point (x, y).
Why: This determines which equation to use: direct substitution or solve for b first.
Step 2: If Given m and b, Write Directly
If both slope and y-intercept are known, substitute directly into y = mx + b.
Why: When m and b are given, no solving is needed; the form is complete.
Step 3: If Given m and Point (x, y), Substitute in y = mx + b
Use y = mx + b with the point's coordinates to solve for b.
Why: The point satisfies the line equation, allowing us to determine the intercept.
Step 4: Rearrange to Solve for b
Isolate b by computing: b = y - mx (subtracting mx from both sides).
Why: Algebraic rearrangement yields the y-intercept from the point and slope.
Step 5: Write the Final Equation
Combine m and b into the form y = mx + b (or y = mx - |b| if b is negative).
Why: The final form is standardized and ready for graphing or further analysis.
The slope-intercept form is a way to write the equation of a line:y = mx + bWhere m is the slope and b is the y-intercept.
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