Question

mrs. rossano asked her students to explain why (3, -4) is a solution to 2y + 3x = 1. three student responses are given below. andrea: \when the equation is graphed on a calculator, the point can be found within its table.\ bill: \substituting x = 3 and y = -4 into the equation makes it true.\ christine: \the graph of the line passes through the point (3, -4).\ which students are correct? 1) andrea and bill, only 2) bill and christine, only 3) andrea and christine, only 4) andrea, bill, and christine

Explanation:

• Andrea: The table of a graphed linear equation (on a calculator) lists points \((x,y)\) that satisfy the equation. So if \((3, - 4)\) is in the table, it's a solution.
• Bill: The definition of a solution to an equation \(ax + by=c\) (or in this case \(2y + 3x = 1\)) is a pair \((x,y)\) that makes the equation true when substituted. Substituting \(x = 3\) and \(y=-4\) into \(2y+3x\): \(2(-4)+3(3)=-8 + 9=1\), which matches the right - hand side. So Bill is correct.
• Christine: A point \((x,y)\) is on the graph of a linear equation \(Ax+By = C\) if and only if it is a solution to the equation. So if the graph passes through \((3,-4)\), then \((3,-4)\) is a solution.

All three students are correct.

Answer:

1. Andrea, Bill, and Christine