Question

How do you find the slope and intercepts of $x - 2y = 8$?

Answer 1

Given a linear equation. We have to find the slope and intercepts of the given equation. First, we will convert the given equation in standard form of slope intercept equation of line. Then, determine the value of slope by comparing the two equations. Then, determine the x intercept of the equation by substituting zero for y in the equation. Then, determine the y- intercept by substituting 0 for x into the equation.

Formula used:
The slope-intercept form of the equation is given by:
$y = mx + b$
Where $m$ is the slope and $b$ is the intercept

Complete step by step solution:
We are given the equation, $x - 2y = 8$. First, convert the given equation in slope intercept form.
Subtract x from both sides of the equation.
$\Rightarrow x - 2y - x = 8 - x$
On simplifying the inequality, we get:
$\Rightarrow - 2y = - x + 8$
Now, divide both sides of equation by $- 2$
$\Rightarrow \dfrac{{ - 2y}}{{ - 2}} = \dfrac{{ - x}}{{ - 2}} + \dfrac{8}{{ - 2}}$
$\Rightarrow y = \dfrac{1}{2}x - 4$
Now, compare the equation with the standard form of equation $y = mx + b$ to determine the slope.
$\Rightarrow {\text{slope, }}m = \dfrac{1}{2}$
Now, determine the y-intercept by substituting $x = 0$ into the equation $y = \dfrac{1}{2}x - 4$
$\Rightarrow y = \dfrac{1}{2}\left( 0 \right) - 4$
$\Rightarrow y = - 4$
Now, we will determine the x-intercept by substituting $y = 0$ into the equation $y = \dfrac{1}{2}x - 4$
$\Rightarrow \dfrac{1}{2}x - 4 = 0$
Add 4 to both sides of the equation.
$\Rightarrow \dfrac{1}{2}x - 4 + 4 = 0 + 4$
$\Rightarrow \dfrac{1}{2}x = 4$
Multiply both sides of the equation by $2$.
$\Rightarrow 2 \times \dfrac{1}{2}x = 2 \times 4$
$\Rightarrow x = 8$

Hence, the slope of the equation $x - 2y = 8$ is $m = \dfrac{1}{2}$. The x-intercept is $8$ and y-intercept is $- 4$.

Additional Information:
The slope of the linear equation is defined as the change in y values with respect to change in x values. The slope can be either positive or negative.

Note:
In such types of questions the students mainly don't get an approach on how to solve it. In such types of questions students mainly forget to first convert the equation into slope intercept form. Also, students may make mistakes while performing the arithmetic operations.