📐 Gradient Of Straight Line

📋 Name: ____________________ 📅 Date: ____________________ 🏫 Class: Grade 8 ___

🧗‍♀️ MATH ADVENTURE: Scaling the Slope!

Today's Mission: A young architect is designing a wheelchair ramp. The ramp follows a straight line rule. Find the slope (gradient) of that line.

🔍 The Problem
The line that represents the ramp is:

y = 13 x + 7

⚠️ The fraction 1/3 means 1 divided by 3.
Stacked form: 13 (1 on top, 3 at the bottom, like a small staircase).

🧭 What is Gradient?

Gradient tells you how steep a line is.

If the line looks like...	Gradient is...
↗️ (going up, fast)	Big number (e.g., 5)
➡️ (flat)	Zero (0)
↘️ (going down)	Negative number (e.g., -2)

Our ramp goes gently upwards. Let's find its gradient.

🖼️ Diagram (Imagine this)

/|
/ |
/ |
/ |
/ |
/ |
/ |
└───────┘
x → 1 step

Every time you move 1 unit across (x + 1), the line rises only a small amount:
Rise = 1 ÷ 3 = about 0.333...

🔢 Step-by-Step to find the Gradient

Step 1 — General line formula
A straight line is written as:
y = (gradient) × x + (y‑intercept)
Or: y = m x + c
• m = gradient (what we want)
• c = y‑intercept (where line meets the y‑axis)

Step 2 — Compare with our equation
Our equation: y = (1/3) x + 7
Compare with y = m x + c:
• Number next to x = 13 → That is m, the gradient.
• The number on its own 7 is the y‑intercept.

Step 3 — Write the gradient
The gradient = 13

🌍 Real-Life Example

A wheelchair ramp with a gradient of 1/3 means:
For every 3 metres you roll forward, you go 1 metre up.
That’s safe, smooth, and gentle – perfect for hospitals, schools, and homes.

📦 Your Answer Box

Question	Your Answer
Gradient of the line y = (1/3)x + 7	______ / ______

✅ Correct gradient = 13 (one third)

✅ Did You Get It?

• ☐ The gradient is the number with the x.
• ☐ Stacked fraction 13 means 1 divided by 3.
• ☐ The ramp goes up 1 unit every 3 units across.

🏗️ Well done, mathematician! Now go build that ramp 📐

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End of Prompt – CBC Grade 8 | Gradient of a Straight Line | Stacked Fractions