Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
(1)
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (2, 22) and (x₂, y₂ ) = (4, 32) ← 2 ordered pairs from the table
m = [tex]\frac{32-22}{4-2}[/tex] = [tex]\frac{10}{2}[/tex] = 5, thus
y = 5x + c ← is the partial equation
To find c substitute any ordered pair from the table into the partial equation
Using (6, 42), then
42 = 30 + c ⇒ c = 42 - 30 = 12
Thus Table 1 has slope = 5 and y- intercept = 12
(2)
Using (x₁, y₁ ) = 2, 15) and (x₂, y₂ ) = (1,8) ← 2 ordered pairs from the table
m = [tex]\frac{8-15}{1-2}[/tex] = [tex]\frac{-7}{-1}[/tex] = 7, thus
y = 7x + c ← is the partial equation
To find c substitute (3, 22) into the partial equation
22 = 21 + c ⇒ c = 22- 21 = 1
Thus Table 2 has slope = 7 and y- intercept = 1
