Question

I need help with this question asap​

Answer 1

(2, 9 )

Explanation:

We first of all require to find the equation of the line passing through the 2 points.

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (3, 11 ) and (x₂, y₂ ) = (- 2, 1 )

m =
`(1-11)/(-2-3)` =
`(-10)/(-5)` = 2 , then

y = 2x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 11 ) , then

11 = 6 + c ⇒ c = 11 - 6 = 5

y = 2x + 5 ← equation of line

to find which point lies on the line substitute the x- coordinate into the equation and if the result is equal to the y- coordinate then it lies on the line.

(2, 1 ) : y = 2(2) + 5 = 4 + 5 = 9 ≠ 1 ← not on line

(2, 4 ) : y = 2(2) + 5 = 9 ≠ 4 ← not on line

(2, 6 ) : y = 2(2) + 5 = 4 + 5 = 9 ≠ 6 ← not on line

(2, 9 ) : y = 2(2) + 5 = 4 + 5 = 9 ← point lies on line