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Ernie calculated the slope between two pairs of points. He found that the slope between (-1, 4) and (0, 0) is -4. He also found that the slope between (2, 7) and (3, 3) is -4. Ernie concluded that all of these points are on the same line. Use the drop-down menus to complete the statements about Ernie's conclusion.

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MrRoyal

Answer:

Both points do not lie on the same line

Step-by-step explanation:

There's no drop down to select from. However, I'll answer the question based on whether Ernie's conclusion is correct or not.

Given

Point 1:

(-1,4) and (0,0)

Slope: m = -4

Point 1:

(2,7) and (3,3)

Slope: m = -4

To determine if this conclusion is right or wrong; first, we need to determine the equation of both points using:

[tex]y - y_1 = m(x - x_1)[/tex]

For Point 1

[tex](-1,4)[/tex] --- [tex](x_1,y_1)[/tex]

[tex](0,0)[/tex] --- [tex](x_2,y_2)[/tex]

Slope: [tex]m = -4[/tex]

[tex]y - y_1 = m(x - x_1)[/tex] becomes

[tex]y - 4 = -4(x - (-1))[/tex]

[tex]y - 4 = -4(x +1)[/tex]

[tex]y - 4 = -4x -4[/tex]

Add 4 to both sides

[tex]y - 4 + 4= -4x -4 + 4[/tex]

[tex]y = -4x[/tex]

For Point 2:

[tex](2,7)[/tex] --- [tex](x_1,y_1)[/tex]

[tex](3,3)[/tex] --- [tex](x_2,y_2)[/tex]

Slope: [tex]m = -4[/tex]

[tex]y - y_1 = m(x - x_1)[/tex] becomes

[tex]y -7 = -4(x - 2)[/tex]

[tex]y -7 = -4x + 8[/tex]

Add 7 to both sides

[tex]y -7 +7= -4x + 8 + 7[/tex]

[tex]y = -4x + 15[/tex]

Comparing both equations:

[tex]y = -4x[/tex] and [tex]y = -4x + 15[/tex]

Both expressions are not equal.

Hence, both points do not lie on the same line

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