Question

Write the equation of the line that
passes through the two points:
(3, 1) and (7,9)
A) y = 2x - 11
B) y = 2x + 1
C) y = 2x - 5
D) y = 1/2x + 11/2
E) y = 1/2x + 5/2 ​

Answer 1

Answer:

Option C

Step-by-step explanation:

Given:-

The two points (3, 1) and (7,9)

To find:-

Write the equation of the line that

passes through the two points: (3, 1) and (7,9)?

Solution:-

Given points are (3, 1) and (7,9)

Let (x1, y1)=(3,1)=>x1=3 and y1 = 1

Let (x2, y2)=(7,9)=>x2=7 and y2=9

We know that

The equation of a line passing through the points (x1, y1) and (x2, y2) is (y-y1)/(y1-y2)=(x-x1)/(x1-x2)

On Substituting these values in the above formula

=> (y-1)/(1-9) = (x-3)/((3-7)

=> (y-1)/(-8) = (x-3)/(-4)

On applying cross multiplication then

=> (-4)×(y-1) = (-8)×(x-3)

=> -4y+4 = -8x+24

=> -8x+24 + 4y-4 = 0

=> -8x+4y +20 = 0

=> -4(2x-y-5) = 0

=> 2x-y-5 = 0/-4

=>2x-y-5= 0 (or)

=> y = 2x-5

Answer:-

The equation of the line passing through the given two points is y = 2x-5

Used formula:-

The equation of a line passing through the points (x1, y1) and (x2, y2) is (y-y1)/(y1-y2)=(x-x1)/(x1-x2)