Slope Intercept Form Calculator

Slope-Intercept Form

Work with the equation y = mx + b

How To Write Slope-Intercept Form

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.

Detailed Example

Scenario: Line has slope m = 2 and passes through point (3, 7). Write slope-intercept form.
Step 1 - Identify Info: Given m = 2 and point (3, 7); need to find b.
Step 2 - Not Direct: Don't have b directly; must use the point to determine it.
Step 3 - Substitute Point: Using y = mx + b: 7 = 2(3) + b.
Step 4 - Solve for b: 7 = 6 + b, so b = 7 - 6 = 1.
Step 5 - Write Equation: y = 2x + 1 (slope-intercept form complete).
Verification: Check point (3, 7): y = 2(3) + 1 = 6 + 1 = 7 ✓
Result: The equation of the line is y = 2x + 1.
Interpretation: Line crosses y-axis at (0, 1); slope of 2 means rise 2 for every 1 unit of run.

Equation Info

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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