Complete the point slope equation of the line through (-2,6) and (1,1)

y-1 =( -5/3) (x-1)

Step-by-step explanation:

The point slope equation for a line is

y-y1 = m(x-x1)

where m is the slope and (x1, y1) is a point

We need to determine the slope

The formula for slope is

m = (y2-y1)/(x2-x1)

where (x1,y1) and (x2,y2) are points

m = (1-6)/(1--2)

  = (1-6)/(1+2)

    =-5/3

The slope is -5/3

Now we can substitute the slope into the equation for a line.  We can use either point.  I will use (1,1)

y-y1 = m(x-x1)

y-1 =( -5/3) (x-1)

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.