Answer:
Option A is correct
A. Neither
Step-by-step explanation:
Given:
Two points are given (2, 15) and (0, 5)
Let [tex](x_{1}, y_{1})=(2,15)[/tex] and [tex](x_{2}, y_{2})=(0,5)[/tex]
The slope of the line [tex]m=\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex]
Put all known value in above equation.
[tex]m=\frac{5- 15}{0- 2}[/tex]
[tex]m=\frac{-10}{-2}[/tex]
[tex]m=5[/tex]
So the slope of the line [tex]m=5[/tex].
The equation of the is
[tex]y=mx+b[/tex] -------------------(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 [tex]x=0,y=5\ and\ m=5[/tex] in equation 1.
[tex]y=mx+b[/tex]
[tex]5=5(0)+b[/tex]
[tex]5=0+b[/tex]
[tex]b=5[/tex]
Take point (2, 15) to compute the value of b.
Put [tex]x=2,y=15\ and\ m=5[/tex] in equation 1.
[tex]y=mx+b[/tex]
[tex]15=5(2)+b[/tex]
[tex]15=10+b[/tex]
[tex]15-10=b[/tex]
[tex]b=5[/tex]
So the equation of the line is.
[tex]y=mx+b[/tex]
Put m and b value in above equation.
[tex]y=5x+5[/tex]------------(2)
[tex]5x-y=-5[/tex]
add 10 both side in equation 2.
[tex]y+10=5x+5+10[/tex]
[tex]y+10=5x+15[/tex]
[tex]y+10=5(x+3)[/tex]
So the equation of line that passes through the point (2,15) and (0,5) is.
[tex]y=5x+5[/tex] or [tex]5x-y=-5[/tex] or [tex]y+10=5(x+3)[/tex]
Therefore, Neither the following equations represents a line that passes through the points (2,15) and (0,5).
