Question

Paul and Seth know that one point on a line is (4,2) and the slope of the line is -5. Each student wrote a different equation relating x and y . Do the two equations represent the same line ? Construct a mathematical argument to support your answer .

Answer 1

Explanation:

Paul's equation,

Since the given line is passing through a point (4, 2) and slope = -5,

y = mx + b

2 = -5(4) + b

2 = -20 + b

b = 22

Therefore, equation of the line will be,

y = -5x + 22

Seth equation,

Slope of a line passing through two points (x, y) and (4, 2),

m =
`(y_2-y_1)/(x_2-x_1)`

-5 =
`(y-2)/(x-4)`

-5(x - 4) = y - 2

-5x + 20 = y - 2

y = -5x + 22

Therefore, both the equations represent the same line.