The equation of line lm is 5x − y = −4. what is the equation of a line perpendicular to line lm in slope-intercept form that contains point (−3, 2)?

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 5x - y = - 4 into this form

Subtract 5x from both sides

- y = - 5x - 4 ( multiply through by - 1 )

y = 5x + 4 ← in slope- intercept form

with slope m = 5

Given a line with slope m then the slope of a line perpendicular to it is

= - = - , thus

y = - x + c ← is the partial equation

To fond c substitute (- 3, 2) into the partial equation

2 = + c ⇒ c = 2 - =

y = - x + ← in slope- intercept form

47

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.