Answer:
The equation is y = - 3x + 3
Step-by-step explanation:
The slope-intercept form of the linear equation is y = m x + b, where
→ The table has 4 point: (1, 0), (2, -3), (3, -6), (4, -9)
→ We will choose two of them to find the slope
∵ The points (1, 0) and (2, -3) lie on the line
∴ [tex]x_{1}[/tex] = 1 and [tex]x_{2}[/tex] = 2
∴ [tex]y_{1}[/tex] = 0 and [tex]y_{2}[/tex] = -3
→ Substitute these values in the rule of the slope above
∴ [tex]m=\frac{-3-0}{2-1}=\frac{-3}{1}=-3[/tex]
∴ m = -3
→ Substitute the value of the slope in the form of the equation
∴ y = - 3x + b
→ To find b substitute x and y by the coordinates of a point on the line
∵ x = 1 and y = 0
∴ 0 = - 3(1) + b
∴ 0 = - 3 + b
→ Add 3 to both sides
∴ 0 + 3 = -3 + 3 + b
∴ 3 = b
∴ b = 3
→ Substitute the value of b in the form of the equation above
∴ y = -3x + 3
The equation is y = - 3x + 3
