Question

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

Answer 1

(i)

The equation of line is x+7y=0 .

The slope-intercept form of general equation of line Ax+By+C=0 for B≠0 is given by

y=− A B x− C B or y=mx+c (1)

Here m=− A B , and c=− C B .

Rearrange the terms of equation of line.

y=− 1 7 x+0

Compare the above equation with the slope intercept form of equation (1).

m=− 1 7 ,c=0

Thus, the slope intercept form of the line x+7y=0 is y=− 1 7 x+0 . The slope of the line x+7y=0 is − 1 7 and y intercept is 0 .

(ii)

The equation of line is 6x+3y−5=0 .

Rearrange the terms of equation of line.

3y=−6x+5 y= 1 3 ( −6x+5 ) y=−2x+ 5 3

Compare the above equation with the slope intercept form of equation (1).

m=−2,c= 5 3

Thus, the slope intercept form of the line 6x+3y−5=0 is y=−2x+ 5 3 . The slope of the line 6x+3y−5=0 is −2 and y intercept is 5 3 .

(iii)

The equation of line is y=0 .

Compare the above equation with the slope intercept form of equation (1).

m=0,c=0

Thus, the slope intercept form of the line is y=0 . The slope of the line y=0 is 0 and y intercept is 0 .