Question

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

Answer 1

In this question, we have to make a given equation in the form of slope intercept form of a line. It can be done by first subtracting $5x$ from both sides of the equation. Then compare the final equation with the standard slope intercept form of a line and find the slope $m$ and an intercept $c$ on $y$-axis for this equation.
The Slope Intercept Form of a Line:
The equation of a line with slope $m$ and making an intercept $c$ on $y$-axis is $y = mx + c$.

Complete step by step solution:
We know that the slope intercept form of a line is the equation of a line with slope $m$ and making an intercept $c$ on $y$-axis is $y = mx + c$.
Given equation is $5x + y = 4$
So, we have to make a given equation in the form of $y = mx + c$, the equation of a line with slope $m$ and making an intercept $c$ on $y$-axis.
First, subtract $5x$ from both sides of the above equation.
$\Rightarrow y = 4 - 5x$
Reorder $4$ and $- 5x$.
$\Rightarrow y = - 5x + 4$
Now, compare this equation with the standard slope intercept form of a line and find the slope $m$ and an intercept $c$ on $y$-axis for this equation.
Here, $m = - 5$ and $c = 4$.

Therefore, the slope of $5x + y = 4$ is $- 5$.

Note: Slope and $y$-intercept of a line can also be determined by graphing the given equation.
Graph of $4x + 2y - 5 = 0$:

Since, the line $5x + y = 4$ cuts the $y$-axis at $4$.
So, $y$-intercept of a given line is $4$.
We can find the slope of given line by putting $\left( {{x_1},{y_1}} \right) = \left( {0.8,0} \right)$ and $\left( {{x_2},{y_2}} \right) = \left( {0,4} \right)$ in $m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$.
So, slope is
$m = \dfrac{{4 - 0}}{{0 - 0.8}}$
On simplification, we get
$m = - 4 \times \dfrac{{10}}{8}$
$\Rightarrow m = - 5$
So, the slope of the given line is $- 5$.