Answer:
The equation of the line is y = [tex]\frac{3}{2}[/tex] x ⇒ D
Step-by-step explanation:
The form of the linear equation is y = m x + b, where
- m is the slope of the line
- b is the y-intercept (value y at x = 0)
The rule of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where
- (x1, y1) and (x2, y2) are two points on the line
∵ The line passes through the origin (0, 0) and point (4, 6)
∴ x1 = 0 and y1 = 0
∴ x2 = 4 and y2 = 6
→ Substitute them in the rule of the slope above to find it
∵ m = [tex]\frac{6-0}{4-0}=\frac{6}{4}=\frac{3}{2}[/tex]
∴ m = [tex]\frac{3}{2}[/tex]
→ Substitute it in the form of the equation above
∴ y = [tex]\frac{3}{2}[/tex] x + b
∵ The line passes through the origin
∴ The y-intercept = 0
∴ b = 0
→ Substitute it in the equation
∵ y = [tex]\frac{3}{2}[/tex] x + 0
∴ y = [tex]\frac{3}{2}[/tex] x
∴ The equation of the line is y = [tex]\frac{3}{2}[/tex] x
