Linear equations: solve for y

Key Notes :

What is a Linear Equation?

A linear equation is an equation in which:

• Variables have power 1
• Graph is a straight line
• Can be written in the standard form:

ax+by=c

where a,b,c are numbers, x and y are variables.

---

Why Solve for y?

• To rewrite in slope-intercept form:

y=mx+b

where:
m = slope (rate of change)
b = y-intercept (where the line crosses y-axis)

• Makes graphing easier.

---

General Steps to Solve for y

• Find the term containing y.
• Move all other terms to the opposite side (+ becomes −, − becomes +).
• Divide by the coefficient of y to make it y= ….
• Simplify fractions or negatives if needed.

💡 Think-Check: The yyy must be alone on one side, with coefficient 1.

---

Worked Examples

Example 1 – Easy

Solve for yyy:

3x+y=7

Step 1: Move 3x:

y=−3x+7

✅ Check: y alone, in slope-intercept form.

---

Example 2 – Needs Division

Solve for y:

2x−4y=8

Step 1: Move 2x:

−4y=−2x+8

Step 2: Divide by −4:​

y=−2x+8​/−4

Step 3: Simplify:

y=x/2−2

✅ Check: slope = 1/2, intercept = −2.

---

Example 3 – Negative y term

Solve for y:

−y+4x=8

Step 1: Move 4x

−y=−4x+8

Step 2: Multiply by -1:

y=4x−8

✅ Check: slope = 4, intercept = −8.

---

Common Mistakes to Avoid

❌ Forgetting to change the sign when moving a term.
❌ Not dividing all terms when removing a coefficient.
❌ Mixing up slope (m) and intercept (b).

---

Quick Practice – Solve for y

1. 4x+y=10
2. 5x−2y=6
3. 7y+3x=14
4. −y+2x=−5
5. 6y−x=126

---

Challenge Question

If 3x−2y=6, write it in slope-intercept form and identify slope and y-intercept.

---

Learn with an example

let’s practice!