Chapter 2: Introduction to Linear Polynomials

Exercise

Question

Question: 7 (iii)

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Draw the graph of the following equations, and identify its slope and y-intercept. Also, find the coordinates of the point where it cuts the y-axis.

(iii) 5y = 6x - 10

Answer

1
Rewrite the equation in the form y = ax + b
$5y = 6x - 10$
⇒
\text{ $y = \dfrac{6}{5}x - 2$ $\quad$ ${color:#625B5F}[Divide both sides by 5]{/color}$}
2
Choose a few values of x and calculate the corresponding values of y to plot the line.
The table shows some sample values of $x$ and $y$.
$x$
$y$
0
-2
5
4
3
Plot the points and join them to draw the straight line.
Graph of the straight line 5y = 6x - 10
Answer: Graph of the equation 5y = 6x - 10
4
Compare the given equation with y = ax + b to identify the slope and the y-intercept.
\textbf{Answer: Slope = $\dfrac{6}{5}$ and $y$-intercept = -2}
\textbf{Reason: Comparing $y = \dfrac{6}{5}x - 2$ with $y = ax + b$, we get $a = \dfrac{6}{5}$ and $b = -2$}
5
Find the point where the graph cuts the y-axis.
The $y$-intercept is -2, so the graph crosses the $y$-axis when $x = 0$ and $y = -2$. Hence, the point is $(0, -2)$
6
Write the coordinates of the point where the graph cuts the y-axis.
Answer: The graph cuts the $y$-axis at $(0, -2)$
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