SOLUTION
From the question given the following statements to prove are correct, then the last part
The reason is Side-side-side triangle theorem
This theorem states that all three sides of a triangle are congruent (identical) to the corresponding sides of another triangle, then the triangles themselves are also congruent.
Hence the answer is Side-side-side triangle theorem
Answer:
✅The table can be represented by the equation,
✅The relation is a function.
✅The graph of the function is linear.
Step-by-step explanation:
✍️The first statement: The table can be represented by the equation, .
To check if the first statement is correct let's find the equation that can represent the table by finding the slope (m) and y-intercept (b).
Using two pairs, (1, 8) and (2, 12),
Slope = .
Substitute, x = 1, y = 8, and m = 4 into y = mx + b to solve for b.
Thus:
8 = (4)(1) + b
8 = 4 + b
Subtract 4 from each side
8 - 4 = b
4 = b
Plug in the values of b and m into y = mx + b.
Thus, the equation that represents the table would be:
.
✅Therefore, the first statement is correct.
✍️The second statement: The graph of the function is non-linear.
This is NOT TRUE because the equation of the function, , represents the equation of a linear graph in the slope-intercept form. When graphed, it will give us a straight line.
✍️The Third statement: The relation is a function.
This is TRUE because each input value (x-value) has exactly one output value (y-value).
✍️The Fourth statement: The rate of change is NOT constant.
This standby is NOT TRUE.
The rate of change is the slope (m) that we have calculated above to be 4. Between any two pairs, the rate of change remains 4.
Therefore, this statement is not correct.
✍️The Fifth statement: The graph of the function is linear.
This is TRUE. As stated earlier, from the equation generated, it is safe to say that the equation represents graph of a linear function. The graph will be a straight line graph.