Q1.
Let us plot the points (– 3, 6), (– 2, 4), (0, 0), (1, – 2), (2, – 4), (3, – 6) in the coordinate plane on a graph paper as shown in Fig. 2.7. Join the points (– 3, 6) and (3, – 6) using a ruler. Doing so, observe that all five points lie on a straight line. Can you guess the equation of this line by looking at the relationship between the x and y coordinates of each point?
Answer
In every listed point the y-coordinate is −2 times the x-coordinate.
| x | −3 | −2 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|
| y | 6 | 4 | 0 | −2 | −4 | −6 |
| y ÷ x | −2 | −2 | — | −2 | −2 | −2 |
Equation of the line: y = −2x
Why this is the right form: the ratio y/x is the same for every point, so y is a constant multiple of x — that constant is the slope, here −2. Because there is no constant term, the point (0, 0) satisfies the equation, and indeed the line passes through the origin. The negative slope shows itself in the picture: as x moves right, y comes down, so the line falls from upper left to lower right.
Check it yourself: substitute the point that was not used to draw the line, say (−2, 4): −2(−2) = 4. ✓ A single failed check would mean the guessed equation is wrong.