Question

Beatrice calculated the slope between two pairs of points.

She found that the slope between (-3, -2) and (1, 0) is 12.
She also found that the slope between (-2, -1) and (4, 2) is 12.

Beatrice concluded that all of these points are on the same line.

Use the drop-down menus to complete the statements about Beatrice's conclusion.

Answer 1

Beatrice concluded that all of these points are on the same line is false statement.

Solution:

Given that,

Beatrice calculated the slope between two pairs of points

She found that the slope between (-3, -2) and (1, 0) is

She also found that the slope between (-2, -1) and (4, 2) is

Beatrice concluded that all of these points are on the same line

The points are on the lines with the same slopes.

We know that, two parallel lines will also have the same slopes

Therefore,

Beatrice need to find the y-intercept of the equation of the lines

If the y-intercept of the equation of lines is same in both cases,

Then this means that all 4 points are on the same line

Or else, they are two different lines which are parallel

Find the y intercept of (-3, -2) and (1, 0)

The slope intercept form is given as:

y = mx + c ------ eqn 1

where, "m" is the slope and "c" is the y intercept

Substitute m = 1/2 and (x, y) = (1, 0) in eqn 1

Thus y intercept is -1/2

Find the y intercept of line of (-2, -1) and (4, 2)

Substitute m = 1/2 and (x, y) = (4, 2) in eqn 1

Thus y intercept is 0

The two lines, have same slope but ,different y intercept which means lines are parallel

So, Beatrice concluded that all of these points are on the same line is false statement.

THANKS

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Explanation:

Answer 2

Beatrice concluded that all of these points are on the same line is false statement.

Solution:

Given that,

Beatrice calculated the slope between two pairs of points

She found that the slope between (-3, -2) and (1, 0) is
`(1)/(2)`

She also found that the slope between (-2, -1) and (4, 2) is
`(1)/(2)`

Beatrice concluded that all of these points are on the same line

The points are on the lines with the same slopes.

We know that, two parallel lines will also have the same slopes

Therefore,

Beatrice need to find the y-intercept of the equation of the lines

If the y-intercept of the equation of lines is same in both cases,

Then this means that all 4 points are on the same line

Or else, they are two different lines which are parallel

Find the y intercept of (-3, -2) and (1, 0)

The slope intercept form is given as:

y = mx + c ------ eqn 1

where, "m" is the slope and "c" is the y intercept

Substitute m = 1/2 and (x, y) = (1, 0) in eqn 1

`0 = (1)/(2) * 1 + c\\\\c = (-1)/(2)`

Thus y intercept is -1/2

Find the y intercept of line of (-2, -1) and (4, 2)

Substitute m = 1/2 and (x, y) = (4, 2) in eqn 1

`2 = (1)/(2) * 4 + c\\\\2 = 2 + c\\\\c = 0`

Thus y intercept is 0

The two lines, have same slope but ,different y intercept which means lines are parallel

So, Beatrice concluded that all of these points are on the same line is false statement.