Given 8y — 6x =8 :

a) transform the equation into slope-intercept form.

b) find the slope and y-intercept of the line.

c) what is the slope of a line parallel to this line?

d) what is the slope of a line perpendicular to this line ?

e) find the equation, in point-slope form, of the line that is perpendicular to this line and passes through the point (0,2).

Step-by-step explanation:

A:  slope-intercept form:  Solve 8y — 6x =8 for y, as follows:  8y = 6x + 8, so that y = (3/4)x + 1.

B:  Slope:  3/4; y-intercept:  (0, 1)

C:  Any line parallel to this line has the same slope, namely, 3/4.

D:  Any line perpendicular to this line has a slope that is the negative reciprocal of 3/4; that is, the slope of the perp. line is -4/3.

x² + 11x + 18 < 0  

[-11 ± sqrt(121 - 72)]/2 = (-11 ± 7)/2  

solution: (-9, -2)

step-by-step explanation:

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!