Question

Use a graph to determine whether the given three points seem to lie on the same line. If they do, prove algebraically that they lie on the same line and write an equation of the line. $$ (4,-2),(-1,2),(-8,9) $$

Short answer

The points (4,-2),(-1,2),(-8,9) do not lie on the same line.

Step-by-step solution

Calculating the Slope between each pair of points

The slope can be calculated using the formula \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\). Here \(x_{1},y_{1}\) are the coordinates of the first point and \(x_{2}, y_{2}\) are the coordinates of the second. \n Slope between Point 1 and Point 2: \(\frac{2 - (-2)}{-1 - 4} = -\frac{4}{-5} = 0.8\).\n Slope between Point 2 and Point 3: \(\frac{9 - 2}{-8 - (-1)} = \frac{7}{-7} = -1\).\n Slopes are not equal, hence determined that the points don't lie on the same line.

Graphical representation

Use the coordinates of the points to draw them on a graph. Upon drawing, you can also discern visually that the three points do not lie on the same line.