write the equation for a line in point-slope form and in slope-intercept form. parallel to 3x-4y=12 and passes through (8,3).

Answer 1

Point-slope form:
(y-y1)=m(x-x1)
Slope intercept form:
y=mx+b
b is the y-intercept, and m is the slope.

In the given case, m can be evalauated from the given parellel line by transforming it to slope intercept form:
3x-4y=12
y=(3/4)x - 3
so m=(3/4)

Point-slope form:
(x1,y1) = (8,3)
substitute (x1,y1) and m in the point slope form equation and voilà!

Expand the point slope form of the equation and normalize the coefficient of y to 1 to get the slope-intercept form of the equation.

Substitute (8,3) in both equations to make sure that each balances, i.e. the line passes through the given point.