A car traveled 261 miles on 9 gallons of gas. The same car also traveled 145 miles on 5 gallons of gas. If the ordered pairs for this relationship are (gallons, distance), what is the slope of the line through these two ordered pairs?

slope = 29

Step-by-step explanation:

Given that

the ordered pairs for this relationship are (gallons,  distance)

it means on coordinate plane

x represents gallons

y represents distance

thus,

two point on plane will be

A car traveled 261 miles on 9 gallons of gas

miles = 261 ---let it be represented by x1

gallons = 9---let it be represented by y1

(x1,y1) = (9,261)

miles = 145 ---let it be represented by x2

gallons = 5---let it be represented by y2

(x2,y2) = (5,145)

slope of two points (x1,y1) and (x2,y2) is given by

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

thus, slope of the above ordered pair

m = (145-261)/(5-9) = -116/-4 = 29

Thus, slope of the line through these two ordered pairs is 29.

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!