Explain whether the points (−13, 4), (−7, 3), (−1, 2), (5,1), (11,0), (17,−1) represent the set of all the solutions for the equation y=−16x+116.
Yes, because all the solutions of y=−16x+116 need to be integer values for x and y.
Yes, because all of the points that are listed are on the line y=−16x+116.
No, because the point (17,−1) is not on the line that represents the equation y=−16x+116.
No, because the set of all solutions of y=−16x+116 is represented by the line of the equation.
C. This is true. In fact, none of the points is on the line.
D. Also no, because the equation is satisfied by many numbers not listed.
Yes, because all of the points (−13, 4), (−7, 3), (−1, 2), (5,1), (11,0), (17,−1) are on the line y = −16x+116.
The correct answer is: Yes, because all the solutions of y=−16x+116 need to be integer values for x and y.
To explain why, let's look at the equation y=−16x+116. This equation is in the form y=mx+b, where m is the slope of the line and b is the y-intercept. In this case, the slope is -16 and the y-intercept is 116.
To determine if a set of points represents all the solutions of an equation, we need to check if each point satisfies the equation. Let's verify this for the given set of points.
First, let's substitute the x and y values of the first point (-13, 4) into the equation:
4 = -16*(-13) + 116
4 = 208 + 116
4 = 324
As we can see, the equation is not satisfied by the first point, which means it does not represent a solution for the equation.
Let's repeat this process for the other points to see if they satisfy the equation.
For the second point (-7, 3):
3 = -16*(-7) + 116
3 = 112 + 116
3 = 228
Again, the equation is not satisfied by this point, so it does not represent a solution.
Continuing this process for all the points, we find that none of them satisfy the equation. Therefore, the set of points (−13, 4), (−7, 3), (−1, 2), (5,1), (11,0), (17,−1) does not represent the set of all solutions for the equation y=−16x+116.