Question

Find the equation of the linear function represented by the table below in slope-intercept form.

Answer 1

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

• m is the slope of the line

• b is the y-intercept

• The rule of the slope is  $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

→ 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

∴ $x_{1}$ = 1 and $x_{2}$ = 2

∴ $y_{1}$ = 0 and $y_{2}$ = -3

→ Substitute these values in the rule of the slope above

∴ $m=\frac{-3-0}{2-1}=\frac{-3}{1}=-3$

∴ 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