Question

true or false: if a pair of numbers makes x + y = 1 true, it will be located on the line that has been graphed. false true rewatch submit

Explanation:

Step1: Recall the equation of a line

The equation \( x + y = 1 \) can be rewritten in slope - intercept form (\( y=mx + b \)) as \( y=-x + 1 \). This is a linear equation, and by the definition of the graph of a linear equation, all the ordered pairs \((x,y)\) that satisfy the equation \( x + y = 1 \) (or \( y=-x + 1 \)) lie on the line represented by this equation.

Step2: Analyze the statement

The statement says that if a pair of numbers (an ordered pair \((x,y)\)) makes \( x + y = 1 \) true, then it will be located on the line that has been graphed (presumably the line \( y=-x + 1 \)). Since the graph of a linear equation \( Ax+By = C\) (in this case \( A = 1\), \( B = 1\), \( C = 1\)) consists of all the points \((x,y)\) that satisfy the equation, the statement is true.

Answer:

True