Answer:
(1) y = x - 2 , (2) y = - [tex]\frac{2}{3}[/tex] x + 5
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 )
(1)
calculate the slope m, using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
let (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (2, 0) ← 2 points on the line
substitute these values into the formula for m
m = [tex]\frac{0-(-2)}{2-0}[/tex] = [tex]\frac{0+2}{2}[/tex] = [tex]\frac{2}{2}[/tex] = 1
The line crosses the y- axis at (0, - 2 ), then c = - 2
y = x - 2 ← equation of line
(2)
calculate the slope m, using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
let (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (3, 3) ← 2 ordered pairs from the table
substitute these values into the formula for m
m = [tex]\frac{3-5}{3-0}[/tex] = [tex]\frac{-2}{3}[/tex] = - [tex]\frac{2}{3}[/tex]
the line crosses the y- axis at (0, 5 ) ← ordered pair from the table so c = 5
y = - [tex]\frac{2}{3}[/tex] x + 5 ← equation of linear function
