Ch 4 covers linear equations with two variables in the form ax + by + c = 0. Students learn that such equations have infinitely many solutions, each representable as a point on a straight line, and master graphing these equations.
An equation of the form ax + by + c = 0, where a, b, c are real numbers and a, b are not both zero, is a linear equation in two variables. A solution is an ordered pair (x, y) that satisfies the equation. There are infinitely many solutions.
The graph of ax + by + c = 0 is always a straight line. To draw it: find at least two solutions (ordered pairs), plot them, and connect with a straight line. Every point on this line is a solution.
x = a (e.g., x = 3) is a vertical line parallel to y-axis. y = b (e.g., y = −2) is a horizontal line parallel to x-axis. y = mx passes through the origin.
Download: https://ncert.nic.in/textbook/pdf/iemh104.pdf | Complete book: https://ncert.nic.in/textbook/pdf/iemh1ps.zip
For any value of x, you can find a corresponding y (or vice versa) that satisfies the equation. Each pair is a solution and a point on the line. Since a line extends infinitely in both directions, there are infinitely many solution pairs.
Book a Trial + Diagnostic session. Get a personalized Learning Path with clear milestones, tutor match, and a plan recommendation — all within 24 hours.
Book Trial + Diagnostic →