Question

Reduce the following equations into slope -intercept form and find their slopes and the $y$ -intercepts.
A. $x + 7y = 0$ ,
B. $6x + 3y - 5 = 0$ ,
C. $y = 0$ .

Answer 1

Hint : First to find the slope-intercept form the formula for the slope-intercept form is the value of $y$ - axis is equal to product of slope and $x$ -axis and intercept. So need to write all the above equations in the slope intercept form.

Complete step-by-step answer :
Given:
For the first problem we have the equation is $x + 7y = 0$ .
For the second problem we have the equation is $6x + 3y - 5 = 0$ .
For the third problem we have the equation is $y = 0$ .
The general formula for the slope – intercept form is $y = mx + c$ .
Where $m$ is the slope and $c$ is the intercept.

i)
The given equation is $x + 7y = 0$ .
Now, we will add $- 7y$ both sides to the above equation we obtain,
$x + 7y - 7y = 0 - 7y$
Since $7y$ and $- 7y$ get cancelled we obtain,
$x = - 7y$
Multiply $- 1$ both sides to the above equation,
$7y = - x$
Then, multiply both sides by $\dfrac{1}{7}$ we obtain,
$y = - \dfrac{x}{7} + 0$
The slope for the above equation is $m = \dfrac{{ - 1}}{7}$ .
The intercept for the equation is $0$ .
The slope -intercept form for the equation $x + 7y = 0$ is $y = - \dfrac{x}{7} + 0$ .

ii)
The given equation is $6x + 3y - 5 = 0$ .
Adding $- 3y$ both sides to the above equation we obtain,
$6x + 3y - 3y - 5 = - 3y$
Since $3y$ nd $- 3y$ get cancelled we obtain,
$6x - 5 = - 3y$
Multiply $- 1$ both sides to the above equation,
$3y = - 6x + 5$
Then, multiply both sides by $\dfrac{1}{3}$ we obtain,
$y = - \dfrac{{6x}}{3} + \dfrac{5}{3}$
The slope for the above equation is $m = - \dfrac{6}{3}$ .
The intercept for the equation is $\dfrac{5}{3}$ .
The slope - intercept form for the equation $6x + 3y - 5 = 0$ is $y = - \dfrac{{6x}}{3} + \dfrac{5}{3}$ .

iii)
The slope -intercept form is $y = 0$ .
Where, $m = 0$ and intercept is $0$ .

Note : If $x = 0$ then in the slope-intercept form the slope will be $1$ and intercept is $0$ . If the slope is not given, then determine the slope and intercept and substitute in the general formula.