Question

Line contains the points (0,4) and (2,0). Show that the points (-25,81) does or does not lie on line

Answer 1

(- 25, 81) does not lie on the line

Explanation:

We can use the slope m to determine if (- 25, 81) lies on the line or not

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (2, 0)

m =
`(0-4)/(2-0)` =
`(-4)/(2)` = - 2

now if (- 25, 81) lies on the line then the slope between (- 25, 81) and either of the 2 points on the line should equal - 2

(x₁, y₁ ) = (- 25, 81) and (x₂, y₂ ) = (2, 0)

m =
`(0-81)/(2+25)` =
`(-81)/(27)` = - 3

The slopes are not equal hence (-25, 81) does not lie on the line

Answer 2

`\text{Step 1:}\\\\\text{Find the equation of the line passing through the points}\\\\\text{The slope-intercept form:}\ y=mx+b\\\\m-slope\\b-y-intercept\to(0,\ b).\\\\\text{We have the points:}\\(0,\ 4)-y-intercept\to b=4\\(2,\ 0)-x-intercept\\\\\text{Therefore we have the equation:}\ y=mx+4.\\\\\text{The formula of a slope}\\\\m=(y_2-y_1)/(x_2-x_1)\\\\\text{put the coordinates of the points:}\\\\m=(0-4)/(2-0)=(-4)/(2)=-2\\\\\text{Therefore we have}\ \boxed{y=-2x+4}`

`\text{Step 2:}\\\\\text{Put the coordinates of the point (-25, 81) to the equation of a line}\\\text{and check equality}\\\\y=-2x+4,\ x=-25,\ y=81\\\\-2x+4\to-2(-25)+4=50+4=54\\eq81`

Answer: The point does not lie on a line.