Question

Reduce the following equations into slope-intercept form and find their slopes and the y-intercepts. 
(i) \(x + 7y = 0 \)
(ii) \(6x + 3y - 5 = 0 \)
(iii) \(y = 0\)

Answer 1

(i)The given equation is \(x + 7y = 0\)

It can be written as 

\(y =\frac{-1}{7}x + 0............(1)\)

This equation is of the form \(y = mx + c\), where \(m = \frac{-1}{7}\) and \(c = 0\)

Therefore, equation (1) is in the slope-intercept form, where the slope and the y-intercept are \(\frac{-1}{7}\) and 0 respectively.

 

(ii) The given equation is  \( 6x + 3y – 5 = 0\)

It can be written as \(y=\frac{1}{3}(-6x+5)\)
\(y=-2x +\frac{ 5}{3}.........(2)\)

This equation is of the form \(y = mx + c,\) where  \(m =-2\)  and \(c = \frac{5}{3}.\)

Therefore, equation (2) is in the slope-intercept form, where the slope and the y-intercept are -2 and \(\frac{5}{3}\) respectively.

 

(iii) The given equation is \( y = 0\)

It can be written as  \(y = 0 × x + 0.....(3)\)

This equation is of the form\( y = mx + c\), where \(m = 0\) and \(c = 0\). 
Therefore, equation (3) is in the slope-intercept form, where the slope and the y-intercept are 0 and 0 respectively.