Answer:
The equation that represents the line that passes through the given points is y - 1 = [tex]\frac{5}{3}[/tex] (x - 3) ⇒ A
Step-by-step explanation:
The point-slope form of the linear equation is y - y1 = m(x - x1), where
- m is the slope of the line
- (x1, y1) is a point on the line
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 points (3, 1) and (6, 6)
∴ x1 = 3 and y1 = 1
∴ x2 = 6 and y2 = 6
→ Substitute them in the rule of the slope to find it
∵ m = [tex]\frac{6-1}{6-3}=\frac{5}{3}[/tex]
∴ m = [tex]\frac{5}{3}[/tex]
→ Substitute the value of x1, y1, and m in the form of the equation above
∵ y - 1 = [tex]\frac{5}{3}[/tex] (x - 3)
∴ The equation that represents the line that passes through the given
points is y - 1 = [tex]\frac{5}{3}[/tex] (x - 3)
