Equation slope

Question

Write and equation slope intercept form and standard form of a line that passes through (-1,4) and perpendicular to 2x=-3y+8??

Answer 1

We need to find the slope of the line 2x=-3y+8 first 

 

to do this we change it to the slope intercept form:

 

2x = -3y +8 

 

--> 2x +3y = 8 

-->3y=-2x+8

divide both side by 3 we have 

y=-2/3x + 8 --> this is slope intercept form

then the slope of this line is -2/3

The line we need to find perpendicular to the line which has slope -2/3. So, it has slope =  3/2

 (recall if two lines are perpendicular the product of slope is -1)

 

The line which has slope 3/2 and pass through (-1,4) has equation 

 

y - 4 = 3/2(x+1)

y - 4 = 3/2x +3/2

y= 3/2x + 3/2 +4

--> y = 3/2x + 11/2