Answer:
The statement that reads: "If the graphs of two functions do not intersect at exactly one point, then the two linear functions have the same coefficients of x."
Step-by-step explanation:
The first two statements go from a statement on the values of the coefficients of x (thus, associated with statement "p") and imply some statement regarding the intersection of graphs (associated with statement "q"). Therefore the implication goes in the opposite direction to q --> p
The third statement is the negative of q --> p , but logically implies the same.
The fourth statement is in fact q --> NOp, and therefore does NOT imply the same as q --> p
The correct statement is the third on in the list.
If two linear functions have different coefficients of x, then the graphs of the two functions intersect at exactly one point.
A linear function is a function that represents a straight line on the coordinate plane. The general equation for a linear function is written as,
y = ax + b
where y is the output of the function, a is the coefficient of x, x is the input of the function, and b is a constant.
As we know about linear function, now, if the value of a is the same while the value of c is different then two of the linear functions are parallel, while if the two of the functions have the value of 'a' different then the slope of the two lines will be different, therefore, the line will be intersecting at a single point.
Hence, If two linear functions have different coefficients of x, then the graphs of the two functions intersect at exactly one point.
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