Question

How do you find the slope given $2y = 7$?

Answer 1

Hint: Write the given equation in the form of slope-intercept form. Compare both the slope-intercept formula and the given equation which is written in slope-intercept form to find $m$ which will be the slope of the given line.

Formula used:
Any straight line can be written in slope-intercept form, $y = mx + b$,
where $m$ is said to be the slope of the line $(m = \tan \theta )$ and $b$ is the intercept.

Complete step-by-step answer:
The given linear equation is,$2y = 7$
The slope-intercept form is $y = mx + b$,
where $m$ is the slope of the line and $m = \tan \theta $; $b$ is the $y$-intercept.
Write the given equation in terms of $y$.
$ \Rightarrow y = \dfrac{7}{2}$
Now, for better understanding write the equation along with the $x$ term to easily compare it with the slope-form.
$ \Rightarrow y = (0)x + \dfrac{7}{2}$
Comparing it with the slope-equation, $y = mx + b$
$ \Rightarrow m = 0;b = \dfrac{7}{2}$
$m$ is considered to be the slope of the equation and $b$ as the $y$-intercept, the constant.
$\therefore $The slope of the equation, $2y = 7$ is $0$.

This also means that the equation $2y = 7$ when plotted on a graph gives a straight line parallel to the $x$ axis.

Additional information: Whenever the slope of a line $m$ is $\infty $ it indicates that the equation is a straight line parallel to the $y$ axis. If the slope of the line $m$ is $0$, then it indicates that the equation is a straight line parallel to the $x$ axis. The slope is also known as the “gradient”.

Note:
The slope of the above equation can also be found by using the alternate slope formula which requires at least two coordinates to find the slope.
The formula is,
$\Rightarrow$$m = \dfrac{{({y_2} - {y_1})}}{{({x_2} - {x_1})}}$
where $({x_1},{y_1})$ are the coordinates of one point which satisfies the equation,$2y = 7$
and $({x_2},{y_2})$are the coordinates of the second point which satisfy the same equation.
For any value of $x$,$y = \dfrac{7}{2}$. So, the values of ${y_1},{y_2}$ are going to be the same.
$ \Rightarrow m = \dfrac{{(\dfrac{7}{2} - \dfrac{7}{2})}}{{({x_2} - {x_1})}}$
$ \Rightarrow m = \dfrac{0}{{({x_2} - {x_1})}} = 0$
$\therefore $The slope of the line equation, $2y = 7$ is $0$.