Slope-intercept form: write an equation

Key Notes:

What is Slope-Intercept Form?

A line can be written in the slope-intercept form:

y = mx + b

where:

• m = slope of the line (steepness)
• b = y-intercept (the point where the line crosses the y-axis)

---

Formula Recap: Slope

The slope between two points (x₁,y₁)​ and (x₂,y₂) is:

m=y₂−y₁/x₂−x₁

---

Writing the Equation – Given Slope and Y-Intercept

If you know mmm and bbb, simply substitute into:

y=mx+b

Example:
Slope m=3, y-intercept b=−2

y=3x−2

---

Writing the Equation – Given Slope and a Point

If you know mmm and a point (x₁,y₁), use the point-slope form first: y−y₁=m(x−x₁)

Then, rearrange into y=mx+b.

Example:
Slope m=−4point (2, 5)

y−5=−4(x−2)

y−5=−4x+8

y=−4x+13

---

Writing the Equation – Given Two Points

1.Find the slope mmm using:

m=y₂−y₁/x₂−x₁

2.Use one of the points and point-slope form to find b.

3.Write the final equation in slope-intercept form.

Example:
Points (1, 2) and (3, 6)
Step 1:

m=6−2/3−1=4/2=2

Step 2: Using (1, 2):

y−2=2(x−1)

y = 2x + 0

Final:

y=2xy

---

Special Cases

• Horizontal line: slope m=0 → equation is y=b
• Vertical line: slope is undefined → cannot be written in y=mx+b

---

Practice Problems

1. Write the equation of a line with slope 5 and y-intercept -3.

2. Write the equation of a line with slope -2 passing through (4, 7).

3. Find the equation of the line passing through (0, -2) and (5, 3).

4. A line has slope 34\frac{3}{4}43​ and passes through (2, -1). Write its equation.

Learn with an example