Question

8. Determine the equation of line through the point (3, - 4) and the point of intersection of
the lines x + y = 3 and x - y = 1.​

Answer 1

Answer:

y = - 5x  + 11

Step-by-step explanation:

$\left \{ {{x+y=3} \atop {x-y=1}} \right.$

(1) + (2)

2x = 4 ⇒ x = 2

2 + y = 3 ⇒ y = 1

(2, 1) and (3, - 4)

Slope of line passing through two those points is

m = $\frac{y_{1} -y_{2} }{x_{1} -x_{2} }$

m = (- 4 - 1) ÷ (3 - 2)  = - 5

Point-slope equation of the line with the certain slope and passing through certain point $(x_{1} , y_{1} )$ is

$y - y_{1} = m(x - x_{1} )$

y - 1 = - 5(x - 2)

y = - 5x  + 11