Question

How do you find the slope and intercept for $x-4y=-8$ ?

Answer 1

In this question we will rearrange the given expression by isolating the term $y$ and write in the term of the general equation of the line which is denoted as $y=mx+b$, where $m$ is the slope of the equation and $b$ is the intercept of the line and then plot the graph for the equation.

Complete step by step answer:
We have the given equation as:
$\Rightarrow x-4y=-8$
On transferring the term $x$ from the left-hand side of the equation to the right-hand side of the equation, we get:
$\Rightarrow -4y=-8-x$
On multiplying both the sides of the expression by $-1$, we get:
$\Rightarrow 4y=8+x$
On transferring the term $4$ from the left-hand side of the equation to the right-hand side of the equation, we get:
$\Rightarrow y=\dfrac{8}{4}+\dfrac{x}{4}$
On rearranging the terms in the above expression, we get:
$\Rightarrow y=\dfrac{1}{4}x+\dfrac{8}{4}$
On simplifying the terms, we get:
$\Rightarrow y=\dfrac{1}{4}x+2$
Now the above expression is in the form of the general equation of a line $y=mx+b$ therefore, we can deduce that the slope of the line $m=\dfrac{1}{4}$ and the intercept of the equation $b=2$, which are the required solution and the graph of the equation can be plotted as:

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.