Write the equation of a line described below in slope intercept form

Question

perpendicular to 7x-3y=4 passing through (1,-2)

Answer 1

First, we have to rearrange the given line into slope-intercept form:

 

7x - 3y = 4

-3y = -7x + 4

y = (7/3)x - 4/3

 

We know that a line perpendicular to this line will have a slope that is a negative reciprocal (i.e., m = -3/7).  Next, set up an equation to find the y-intercept:

 

y = mx + b

-2 = (-3/7)(1) + b

-2 = -3/7 + b

-2 + 3/7 = b

-14/7 + 3/7 = b

-11/7 = b

 

Now, we have the slope of our new line and its y-intercept:

 

y = (-3/7)x - 11/7