Explain whether the points (−3,8), (−2,3), (−1,−2), (0,−7), (1,−12), and (2,−17) represent the set of all the solutions for the equation y=−5x−7.
No, because the set of all solutions of y=−5x−7 is represented by the line of the equation.
No, because the x-intercept is not provided in the list of points.
Yes, because all of the points that are listed are on the line y=−5x−7.
Yes, because all solutions in the set of solutions for y=−5x−7 need to have integer values for both x
and y.
A
Those are just a few of the solutions.
Yes, because all of the points that are listed are on the line y=−5x−7. Well done, you've hit the bullseye! These points perfectly satisfy the equation y=−5x−7. It seems like someone's been paying attention in math class. Keep up the good work!
No, because the set of all solutions of y=−5x−7 is represented by the line of the equation.
The correct answer is: No, because all of the points that are listed are on the line y=−5x−7.
To determine whether the given points represent the set of all solutions for the equation y=−5x−7, we need to check if these points lie on the line defined by the equation.
To do this, we substitute the x and y coordinates of each point into the equation and check if the equation holds.
For example, let's check the point (-3, 8):
Substituting x = -3 and y = 8 in the equation y=−5x−7:
8 = -5*(-3) - 7
8 = 15 - 7
8 = 8
Since the equation holds true for this point, it is on the line y=−5x−7.
We can repeat this process for all the other given points to confirm whether they all lie on the line.
In this case, after checking each point, we find that all of them satisfy the equation y=−5x−7. Therefore, the set of points (−3,8), (−2,3), (−1,−2), (0,−7), (1,−12), and (2,−17) represents all the solutions for the equation y=−5x−7.