the graph of the linear equation passes through the points (-1,4) and (2,1) find the values of p and q - Maths - Linear Equations in Two Variables

Question

the graph of the linear equation passes through the points
(-1,4) and (2,1) find the values of p and q if the graph also
passes through (p,3) and (q,1) write the equation of the line

ramandeep.singh · Accepted Answer

Let the equation of the line be $a x + b y + c = 0$ .

The line passes through (-1, 4).

$∴ - a + 4 b + c = 0 \Rightarrow c = a - 4 b ..... (1)$

The line also passes through (2, 1).

$∴ 2 a + b + c = 0 \Rightarrow 2 a + b + a - 4 b = 0 (U \sin g (1)) \Rightarrow 3 a - 3 b = 0 ∴ a = b$

Substitute this value in equation (1).

$c = a - 4 b = a - 4 a = - 3 a$

Therefore, the equation of the line is

$a x + a y - 3 a = 0 \Rightarrow x + y - 3 = 0$

As the line passes through (p, 3).

$∴ p + 3 - 3 = 0 \Rightarrow p = 0$

Also, the line passes through (q, 1).

$∴ q + 1 - 3 = 0 \Rightarrow q = 2$

Therefore,

p = 0

q = 2

the graph of the linear equation passes through the points (-1,4) and (2,1) find the values of p and q if the graph also passes through (p,3) and (q,1) .write the equation of the line.