Q2 of 23 Page 230

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).

Slope of the line


⇒ Slope of the line


Equation of line :



⇒ 3(y - 5) = 2(x - 2)


⇒ 2x - 3y + 11 = 0 …Equation (i)


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


2(x + 3) - 3(y + 2) + 11 = 0


⇒ 2x - 3y + 11 = 0


Since it again gives the same equation as (i) so it is a point on this line.


Hence Proved


More from this chapter

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4

Prove that if the point (x1, y1), (x2, y2), (x3, y3) are on a line, so are (3x1 + 2y1,3x1 – 2y1), (3x2 + 2y2,3x2 – 2y2), (3x3 + 2y3,3x3 – 2y3). Would this be true if we take other numbers instead of 3 and 2?

 1

Find the equation of the line joining (1, 2) and (2, 4). In this, find the sequence of y coordinates of those points with the consecutive natural numbers 3, 4, 5, … as the x coordinates.

 3

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

 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.