Answer:
The equation of line a is y = x
The equation of line b is y = [tex]\frac{2}{3}[/tex] 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 = [tex]\frac{y2-y1}{x2-x1}[/tex] , 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 = [tex]\frac{3-0}{3-0}=\frac{3}{3}[/tex]
∴ 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 = [tex]\frac{2-0}{3-0}=\frac{2}{3}[/tex]
∴ m = [tex]\frac{2}{3}[/tex]
→ Substitute in the form of the equation above
∴ y = ([tex]\frac{2}{3}[/tex]) x
∴ y = [tex]\frac{2}{3}[/tex] x
∴ The equation of line b is y = [tex]\frac{2}{3}[/tex] x
