Reduce the following equations into slope-intercept form and find their slopes and the -intercepts.
(i) x + 7y = 0
To reduce to slope-intercept form: x + 7y = 0 7y = -x y = -x/7
Comparing with y = mx + c, we get slope m = -1/7 and y-intercept c = 0.
(ii) 6x + 3y - 5 = 0
To reduce to slope-intercept form: 6x + 3y - 5 = 0 3y = -6x + 5 y = -2x + 5/3
Comparing with y = mx + c, we get slope m = -2 and y-intercept c = 5/3.
(iii) y = 0
This equation is already in slope-intercept form.
Comparing with y = mx + c, we get slope m = 0 and y-intercept c = 0.
Explanation
The slope-intercept form of a line is y = mx + c, where m represents the slope and c represents the y-intercept. To convert any linear equation to this form, isolate y on one side. The coefficient of x becomes the slope, and the constant term becomes the y-intercept.