This document provides solutions to exercises on mathematical thinking, including finding slopes, intercepts, and sketching graphs. It covers topics such as equations and graphs. Suitable for beginners.
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Introduction to Mathematical Thinking Solutions Q1. a)For the points (2,4) and (5,6) , slope=dy dx=6−4 5−2=2 3 →2 3=y−4 x−2 ∴y=2 3x+8 3 b)For the points (4,3) and (-2,5) , slope=dy dx=5−3 −2−4=−1 3 →−1 3=y−3 x−4 ∴y=−1 3x+13 3 Q2. a)For the point (2,1) with gradient 3: slope=3=y−1 x−2 ∴y=3x−5 ¿theformofx a+y b=1,theequationbecomesx (5 3)+y 3=1 ,wherex−intercept,a=5 3∧y−intercept,b=3 b)For the point (-2,1) with gradient1 2: slope=1 2=y−1 x+2 ∴y=1 2x+2 ¿theformofx a+y b=1,theequationbecomesx −4+y 2=1 ,wherex−intercept,a=−4∧y−intercept,b=2
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