Katherine uses $\frac{7}{10}$ of a gallon of red paint to paint $\frac{3}{5}$ of her wall. How many gallons of red paint will she use to paint her whole wall? There is no 5/5

1.167 gallons

Step-by-step explanation:

Given that:

Fraction of red paint used = 7/10 of a gallon

Fraction of wall painted = 3/5

Gallon of paint required to paint the entire wall:

Fraction of entire wall = 1/1

7/10 paint = 3/5 wall

x paint = 1 wall

Cross multiply

(3/5)x = 7/10

Divide both sides by 3/5

3/5x ÷ 3/5 = 7/10 ÷ 3/5

(3/5)x * 5/3 = 7/10 * 5/3

x = 35 / 30

x = 7/6 = 1.167 gallons of red paint

The average rate of change is calculated as the slope of the line between the two points on the graph. Since at x = 1, y = -3, and at x = 3, y = 1, these are the two points which we calculate the slope from. Using the formula

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

m = (1 - (-3))/(3 - 1)

m = 4/2

m = 2

Therefore the slope, or the average rate of change, between these points is 2.