Question

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

Answer 1

Answer:

Option A is correct

A. Neither

Step-by-step 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 $m=\frac{y_{2}- y_{1}}{x_{2}- x_{1}}$

Put all known value in above equation.

$m=\frac{5- 15}{0- 2}$

$m=\frac{-10}{-2}$

$m=5$

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).