Question

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

Answer 1

In this question we will first convert the given linear expression in the general form of the equation of a line which is $y=mx+b$, where $b$ is the $y$ intercept and $m$ is the slope of the line, and then solve for the values for the $x$ intercept and the $y$ intercept to plot the line on the graph.

Complete step by step answer:
We have the expression as $y+4x=5$
We will first convert this expression to the slope intercept form of a line which is $y=mx+b$.
$\Rightarrow y+4x=5$
On transferring the term $4x$ from the left-hand side to the right-hand side, we get:
$\Rightarrow y=5-4x$
The right-hand side can be rearranged and written as:
$\Rightarrow y=-4x+5$
Therefore, the above equation is in the form of $y=mx+b$ where $m$ is the slope of the equation therefore the slope $m=-4$.
Now to plot the graph we need to find the coordinates for the $x$ and $y$ intercept.
From the general format, we know that $b$ is the $y$ intercept of the line therefore $y=5$, which is the $y$ intercept.
Now to calculate the $x$ intercept from the equation we will substitute $y=0$ and solve for $x$.
On substituting $y=0$, we get:
$\Rightarrow 0=-4x+5$
On transferring the term $-4x$ from the right-hand side to the left-hand side, we get:
$\Rightarrow 4x=5$
On transferring the term $4$from the left-hand side to the right-hand side, we get:
$\Rightarrow x=\dfrac{5}{4}$, which is the $x$ intercept.
On plotting the graph by taking the two points as $(0,5)$ and $\left( \dfrac{5}{4},0 \right)$ , we get:

Which is the required solution.

Note: Slope of a line is calculated as the ratio between the vertical change and the horizontal change. It can be also defined as how much the change in one intercept will affect the change in another intercept.
It can be calculated using the formula $m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ where $({{x}_{1}},{{y}_{1}})$ coordinates of first line and $({{x}_{2}},{{y}_{2}})$ are the coordinates of the second line.