Slope-Intercept Form

📖 What is the Slope-Intercept Form?

The slope-intercept form is the most common way to write the equation of a straight line. It immediately tells you two key facts about the line: its slope (steepness) and its y-intercept (where it crosses the y-axis).

y = mx + b

🔤 What Each Variable Means

y

Dependent variableThe output value on the vertical axis

x

Independent variableThe input value on the horizontal axis

m

Slope (rise over run)m = Δy / Δx — positive slope goes up, negative goes down

b

y-interceptThe value of y when x = 0 (where the line crosses the y-axis)

📝 Step-by-Step Example

A line has slope 2 and y-intercept -3. Write its equation and find y when x = 4.

1

Identify m and bm = 2 b = -3

2

Write the equationy = 2x + (-3) → y = 2x - 3

3

Substitute x = 4y = 2(4) - 3 = 8 - 3

✓

Answer: y = 5

When x = 4, the point (4, 5) is on the line.

🧮 Interactive Calculator

Enter slope (m), y-intercept (b), and x to find y

Slope (m)

y-intercept (b)

x value

Result will appear here

💡 Finding Slope Between Two Points

m = (y₂ - y₁) / (x₂ - x₁)

Use this formula when you have two points and need to find the slope before writing the full line equation.

📖 What is the Slope-Intercept Form?

🔤 What Each Variable Means

📝 Step-by-Step Example

🧮 Interactive Calculator

💡 Finding Slope Between Two Points

🔗 Related

🎯 Quick Fact