Question

Which of the following equations represents a line that passes through the points

(2,15) and (0,5)?
À
I. y + 10 = 5(x + 2)
II. 5x – y = -6
A.Neither
B.I only
C.II only
D.I and II​

Answer 1

Option A is correct

A. Neither

Explanation:

Given:

Two points are given (2, 15) and (0, 5)

Let
`(x_(1), y_(1))=(2,15)` and
`(x_(2), y_(2))=(0,5)`

The slope of the line
`m=(y_(2)- y_(1))/(x_(2)- x_(1))`

Put all known value in above equation.

`m=(5- 15)/(0- 2)`

`m=(-10)/(-2)`

`m=5`

So the slope of the line
`m=5`.

The equation of the is

`y=mx+b` -------------------(1)

Where m is the slope of the line and b is y-intercept of the line.

Take point (0, 5) to compute the value of b.

Put
`x=0,y=5\ and\ m=5` in equation 1.

`y=mx+b`

`5=5(0)+b`

`5=0+b`

`b=5`

Take point (2, 15) to compute the value of b.

Put
`x=2,y=15\ and\ m=5` in equation 1.

`y=mx+b`

`15=5(2)+b`

`15=10+b`

`15-10=b`

`b=5`

So the equation of the line is.

`y=mx+b`

Put m and b value in above equation.

`y=5x+5`------------(2)

`5x-y=-5`

add 10 both side in equation 2.

`y+10=5x+5+10`

`y+10=5x+15`

`y+10=5(x+3)`

So the equation of line that passes through the point (2,15) and (0,5) is.

`y=5x+5` or
`5x-y=-5` or
`y+10=5(x+3)`

Therefore, Neither the following equations represents a line that passes through the points (2,15) and (0,5).