Q3 of 23 Page 230

Prove that for any number x, the point (x, 2x + 3) is on the line joining (–1, 1), (2, 7).

Slope of the line


⇒ Slope of the line = 2


Equation of line :


y - 2 = 2(x - 7)


⇒ 2x - y - 12 = 0


Putting x = x and y = 2x + 3 in the above equation we get


2x - (2x + 3) - 12 = 0


which satisfies the above equation


Hence Proved


More from this chapter

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1

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 2

Find the equation of the line joining (–1, 3), (2, 5). Prove that if (x, y) is a point on this line, so is (x + 3, y + 2).

 4

The x coordinate of a point on the slanted (blue) line in the picture is 3.


i) What is its y coordinate?


ii) What is the slope of the line?


iii) Write the equation of the line.

 5

In the picture, ABCD is a square. Prove that for any point on the diagonal BD, the sum of the x and y coordinates is zero.