Question

How do you find the slope of $2x + 4y = 5$ ?

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 solution:
The given linear equation is, $2x + 4y = 5$
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 $y$ .
$\Rightarrow y = \dfrac{{5 - 2x}}{4}$
Comparing it with the slope-equation, $y = mx + b$
$\Rightarrow m = \dfrac{{ - 2}}{4} = \dfrac{{ - 1}}{2};b = \dfrac{5}{4}$
$m$ is considered to be the slope of the equation and $b$ as the $y$-intercept, the constant.

The slope of the equation, $2x + 4y = 5$ is $\dfrac{{ - 1}}{2}$.

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,
$m = \dfrac{{({y_2} - {y_1})}}{{({x_2} - {x_1})}}$
Where $({x_1},{y_1})$ are the coordinates of one point which satisfies the equation, $2x + 4y = 5$
And $({x_2},{y_2})$ are the coordinates of the second point which satisfy the same equation.
When $x = 0$ ,
$\Rightarrow y = \dfrac{{5 - 2x}}{4}$
On substituting the value of $x$
$\Rightarrow y = \dfrac{{5 - 2(0)}}{4} = \dfrac{5}{4}$
One of the coordinates is $\left( {0,\dfrac{5}{4}} \right)$
When $y = 0$ ,
$\Rightarrow (0) = \dfrac{{5 - 2x}}{4}$
$\Rightarrow 5 - 2x = 0$
Bring the degree $1$ to the RHS
$\Rightarrow 2x = 5$
$\Rightarrow x = \dfrac{5}{2}$
Another point that satisfies the equation is $\left( {\dfrac{5}{2},0} \right)$
On substituting in the slope formula,
$\Rightarrow m = \dfrac{{\left( {0 - \dfrac{5}{4}} \right)}}{{\left( {\dfrac{5}{2} - 0} \right)}}$
Evaluate further.
$\Rightarrow m = \dfrac{{ - 5}}{4} \times \dfrac{2}{5}$
$\Rightarrow m = \dfrac{{ - 1}}{2}$
$\therefore$ The slope of the line equation, $2x + 4y = 5$ is $m = \dfrac{{ - 1}}{2}$ .