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.
(ii) 2y = 4x + 7
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Answer
1
Rewrite the equation in the form y = ax + b
$2y = 4x + 7$
⇒
\text{ $y = 2x + \dfrac{7}{2}$ $\quad$ ${color:#625B5F}[Divide both sides by 2]{/color}$}
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
$\dfrac{7}{2} = 3.5$
1
$\dfrac{11}{2} = 5.5$
3
Plot the points and join them to draw the straight line.
Answer: Graph of the equation 2y = 4x + 7
4
Compare the given equation with y = ax + b to identify the slope and the y-intercept.
\textbf{Answer: Slope = 2 and $y$-intercept = $\dfrac{7}{2}$}
\textbf{Reason: Comparing $y = 2x + \dfrac{7}{2}$ with $y = ax + b$, we get $a = 2$ and $b = \dfrac{7}{2}$}
5
Find the point where the graph cuts the y-axis.
\text{The $y$-intercept is $\dfrac{7}{2}$, so the graph crosses the $y$-axis when $x = 0$ and $y = \dfrac{7}{2}$. Hence, the point is $(0, \dfrac{7}{2})$}
6
Write the coordinates of the point where the graph cuts the y-axis.
\textbf{Answer: The graph cuts the $y$-axis at $(0, \dfrac{7}{2}$)}
