Answer:
(- 25, 81) does not lie on the line
Step-by-step 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 = [tex]\frac{0-4}{2-0}[/tex] = [tex]\frac{-4}{2}[/tex] = - 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 = [tex]\frac{0-81}{2+25}[/tex] = [tex]\frac{-81}{27}[/tex] = - 3
The slopes are not equal hence (-25, 81) does not lie on the line
[tex]\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=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{put the coordinates of the points:}\\\\m=\dfrac{0-4}{2-0}=\dfrac{-4}{2}=-2\\\\\text{Therefore we have}\ \boxed{y=-2x+4}[/tex]
[tex]\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\neq81[/tex]
