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.(1 point)
Responses
Yes, because all solutions in the set of solutions for y=−5x−7 need to have integer values for both x
and y
.
Yes, because all solutions in the set of solutions for y equals negative five x minus 7 need to have integer values for both x and y.
No, because the x
-intercept is not provided in the list of points.
No, because the x-intercept is not provided in the list of points.
No, because the set of all solutions of y=−5x−7 is represented by the line of the equation.
No, because the set of all solutions of y equals negative five x minus 7 is represented by the line of the equation.
Yes, because all of the points that are listed are on the line y=−5x−7.
Yes, because all of the points that are listed are on the line y equals negative five x minus 7 .
Yes, because all of the points that are listed are on the line y=−5x−7.
Yes, because all of the points that are listed are on the line y=−5x−7.
The correct answer is: Yes, 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 each point satisfies the equation.
First, let's substitute the x and y values from each point into the equation y=−5x−7 and see if both sides of the equation are equal.
For the point (-3, 8):
Substituting x=-3 and y=8 into the equation y=−5x−7, we get:
8 = −5(-3) - 7
8 = 15 - 7
8 = 8
Since both sides of the equation are equal, the point (-3, 8) satisfies the equation.
Similarly, we can substitute the values for the remaining points and check if they satisfy the equation. Upon checking, we find that all the points satisfy the equation y=−5x−7.
Therefore, we can conclude that all of the given points (−3, 8), (−2, 3), (−1, −2), (0, −7), (1, −12), and (2, −17) represent the set of all solutions for the equation y=−5x−7.