Question

A line passes through the points (-1, -1)

Answer 1

Given:

A line passes through the points (-1, -1) and (5,8).

To find:

Which points lie on the same line?

Solution:

If a line passes through two points, then the equation of the line is:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

A line passes through the points (-1, -1) and (5,8). So, the equation of the line is:

$y-(-1)=\dfrac{8-(-1)}{5-(-1)}(x-(-1))$

$y+1=\dfrac{8+1}{5+1}(x+1)$

$y+1=\dfrac{9}{6}(x+1)$

$y+1=\dfrac{3}{2}(x+1)$

Multiply both sides by 2.

$2(y+1)=3(x+1)$

$2y+2=3x+3$

$2y=3x+3-2$

$y=\dfrac{3}{2}x+\dfrac{1}{2}$

So, the equation of the line is $y=\dfrac{3}{2}x+\dfrac{1}{2}$.

Now, check each point for this equation.

Putting $x=-3$, we get

$y=\dfrac{3}{2}(-3)+\dfrac{1}{2}$

$y=\dfrac{-9+1}{2}$

$y=\dfrac{-8}{2}$

$y=-4$

Similarly,

For $x=9,y=15$.

For $x=1,y=2$.

For $x=4,y=6.5$.

For $x=3,y=5$.

For $x=-2,y=-2.5$.

Therefore, the points (-3,-4), (9,14), (1,2) and (3,5) lie on the same line but the points (4,7) and (-2,-2) are not on that line.