Mathematics

Problem

The straight line passing through the points

(2,4)

and

(6,0)

is the graph of a linear polynomial

y=P(x)

. a. (i) Using these two points, obtain the equation of the line in the form

y=ax+b

. b. (ii) Verify that the point

(6,0)

obtained from part (i) is the zero of the polynomial. c. (iii) Without drawing any additional graph, determine the

y

–intercept of

P(x)

and explain its significance for the graph. d. (iv) Suppose the line is extended to intersect the

x

–axis again after being reflected in the

y

–axis. Write the coordinate of this new intersection point and justify your answer.

Intuitive explanation

The key is recognizing that a linear polynomial is just a line, and you can find its equation from two points using the slope-intercept form. Calculate the slope $m$ from the two given points, then use point-slope form or substitute back into $y = mx + b$ to find the y-intercept $b$ . Once you have $P(x) = mx + b$ , you can evaluate or manipulate it however the problem asks.

Intuitive explanation

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