Problem 69 - College Algebra Essentials

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I used the ordered pairs \((-2,2),(0,0),\) and \((2,2)\) to graph a straight line.

Step-by-Step Solution

Answer

The statement does not make sense. This is because the three points provided, (-2, 2), (0, 0), and (2, 2) do not all lie on the same line.

Step 1: Analyze the Given Points

Check each of the given points. They are (-2, 2), (0, 0), and (2, 2).

Step 2: Check if They Form a Straight Line

To see if they form a straight line, you can use the formula for a line in slope-intercept form: \(y = mx + b\). You should calculate the slope between each pair of points to see if it's consistent. If the slope is not the same between all pairs, then the points don't lie on a straight line.

Step 3: Calculate the Slopes

Calculate the slope between the first two points. The formula for the slope is \((y2-y1) / (x2-x1)\) . Apply this between (-2, 2) and (0, 0). You will get a slope of -1 for these two. Then, compute the slope between the second and third points, (0, 0) and (2, 2), you get a slope of 1. -1 and 1 are not equal, so the points don't make up a straight line.