Question

Each line represents a proportional relationship. Write an equation for each line. Show your work.

Answer 1

Answer:

The equation of line a is y = x

The equation of line b is y =  $\frac{2}{3}$ x

Step-by-step explanation:

The equation of the proportional is y = m x, where

• m is the slope of the line (constant of proportionality)

The rule of the slope of a line is m = $\frac{y2-y1}{x2-x1}$ , where

• (x1, y1) and (x2, y2) are two points on the line

∵ Line a passes through points (0, 0) and (3, 3)

∴ x1 = 0 and y1 = 0

∴ x2 = 3 and y2 = 3

→ Substitute them in the rule of the slope above

∵ m = $\frac{3-0}{3-0}=\frac{3}{3}$

∴ m = 1

→ Substitute in the form of the equation above

∴ y = (1)x

∴ y = x

∴ The equation of line a is y = x

∵ Line b passes through points (0, 0) and (3, 2)

∴ x1 = 0 and y1 = 0

∴ x2 = 3 and y2 = 2

→ Substitute them in the rule of the slope above

∵ m = $\frac{2-0}{3-0}=\frac{2}{3}$

∴ m = $\frac{2}{3}$

→ Substitute in the form of the equation above

∴ y = ($\frac{2}{3}$) x

∴ y =  $\frac{2}{3}$ x

∴ The equation of line b is y =  $\frac{2}{3}$ x