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.
(iv) 3y = 6x - 11
Are any of the lines parallel?
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Answer
1
Rewrite the equation in the form y = ax + b
$3y = 6x - 11$
⇒
\text{ $y = 2x - \dfrac{11}{3}$ $\quad$ ${color:#625B5F}[Divide both sides by 3]{/color}$}
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
-$\dfrac{11}{3} = -3.67$
1
-$\dfrac{5}{3} = -1.67$
3
Plot the points and join them to draw the straight line.
Answer: Graph of the equation 3y = 6x - 11
4
Compare the given equation with y = ax + b to identify the slope and the y-intercept.
\textbf{Answer: Slope = 2 and $y$-intercept = $-\dfrac{11}{3}$}
\textbf{Reason: Comparing $y = 2x - \dfrac{11}{3}$ with $y = ax + b$, we get $a = 2$ and $b = -\dfrac{11}{3}$}
5
Find the point where the graph cuts the y-axis.
\text{The $y$-intercept is $-\dfrac{11}{3}$, so the graph crosses the $y$-axis when $x = 0$ and $y = -\dfrac{11}{3}$. Hence, the point is $(0, -\dfrac{11}{3})$}
6
Write the coordinates of the point where the graph cuts the y-axis.
\textbf{Answer: The graph cuts the $y$-axis at $(0, -\dfrac{11}{3}$).}
7
Compare the slopes of all 4 lines and write which lines are parallel.
Answer: Lines (ii) and (iv) ($2y = 4x + 7$ and $3y = 6x - 11$) are parallel.
\textbf{Reason: The slopes of the four lines are $a_i = -3$, $a_{ii} = 2$, $a_{iii} = \dfrac{6}{5}$, and $a_{iv} = 2$. Since lines (ii) and (iv) have equal slopes and different $y$-intercepts, they are parallel}
