Chapter 2: Introduction to Linear Polynomials
Chapter 2: Introduction to Linear Polynomials
Exercise
Question
Question: 10 (ii)
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17 / 26
The graph of a linear polynomial p(x) passes through the points (1, 5) and (3, 11).
(ii) Find the coordinates where the graph of p(x) cuts the axes.
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Answer
1
Use the polynomial found in the previous question.
$p(x) = 3x + 2$
2
Put x = 0 in p(x) = 3x + 2 to find the point where the graph cuts the y-axis.
\text{$p(x) = 3 × {color:#2E2EFF}0{/color} + 2$}
⇒
$p(x) = 2$
Hence, the graph cuts the $y$-axis at $(0, 2)$
3
Put p(x) = 0 in p(x) = 3x + 2 to find the point where the graph cuts the x-axis.
\text{${color:#2E2EFF}0{/color} = 3x + 2$}
⇒
$3x = -2$
⇒
\text{ $x = -\dfrac{2}{3}$}
\text{Hence, the graph cuts the $x$-axis at $(-\dfrac{2}{3}, 0)$}
4
Write both intercepts.
\textbf{Answer: The graph cuts the $y$-axis at $(0, 2)$ and the $x$-axis at $(-\dfrac{2}{3}, 0)$}