Linear Equations in 5 Minutes — Free Quick Revision
Learn Linear Equations in about 5 minutes — a free bite-sized module with a clear explanation, a worked example and a quick quiz for Indian students.
TL;DR: Learn Linear Equations in about 5 minutes — a free bite-sized module with a clear explanation, a worked example and a quick quiz for Indian students.
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
An equation like y = 2x + 3 is linear. Graph it as a straight line. Solve systems of two equations to find intersection points.
Maths · Class 9 · about 7 minutes
The Idea
A linear equation in two variables has the form ax + by = c (or y = mx + b in slope-intercept form).
Key terms: - Slope (m): How steep the line is. m = (change in y) / (change in x). - y-intercept (b): Where the line crosses the y-axis (when x = 0). - x-intercept: Where the line crosses the x-axis (when y = 0).
To graph y = 2x + 3: - b = 3, so plot (0, 3) on the y-axis. - m = 2, so rise 2 units and run 1 unit right. Plot (1, 5). - Draw a straight line through these points.
To solve a system of two linear equations, find the (x, y) point where both lines intersect. This point satisfies both equations.
Methods: substitution, elimination, or graphing.
Worked Example: Solve a System
Problem. Solve: y = 2x + 1 and y = -x + 4
Solution.
Both equal y, so set them equal: 2x + 1 = -x + 4 3x = 3 x = 1
Substitute back: y = 2(1) + 1 = 3
Solution: (1, 3)
Check: y = -1 + 4 = 3 ✓
Quick Quiz
Answer each one before reading the explanation beneath it.
1. What is the y-intercept of y = -3x + 7?
- -3
- 7 — correct
- 3
- -7
7
2. Two lines are parallel if they have the same ___.
- y-intercept
- slope — correct
- x-intercept
- length
slope
3. What is the slope of the line through (2, 3) and (5, 9)?
- 1
- 2 — correct
- 3
- 6
2
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