Answer:
Car A ⇔ 50 mph
Car B ⇔ 60 mph
Car C ⇔ 55 mph
Step-by-step explanation:
The equation of the proportionality is y = m x, where m is the constant of proportionality we can find it by using the initial values os x and y or by the rule of the slope of a line m = [tex]\frac{y2-y1}{x2-x1}[/tex]
Let us find the constant of proportionality of each car
Car A
∵ The line in the figure passes through points (0, 0) and (1, 50)
∴ x1 = 0 and y1 = 0
∴ x2 = 1, y2 = 50
→ By using the rule of the slope above
∵ m = [tex]\frac{50-0}{1-0}[/tex] = [tex]\frac{50}{1}[/tex]
∴ m = 50
∴ The constant of proportionality of car A is 50 mph
Car B
∵ The equation of proportionality is y = m x
∵ From the given table at x = 1, y = 60
→ Substitute them in the equation to find m
∴ 60 = m (1)
∴ 60 = m
∴ m = 60
∴ The constant of proportionality of car B is 60 mph
Car C
∵ The equation is y = 55x
→ Compare it with the form of the equation of the proportionality
∵ y = m x
∴ m = 55
∴ The constant of proportionality of car C is 55 mph
