Answer:
see explanation
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
(8)
with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (8, 2)
m = [tex]\frac{2-2}{8+3}[/tex] = [tex]\frac{0}{11}[/tex] = 0
A slope of zero indicates the line is horizontal and parallel to the x- axis with equation
y = c
where c is the value of the y- coordinates the line passes through
The line passes through (- 3, 2) and (8, 2) with y- coordinates 2, thus
y = 2 ← equation of line
(9)
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
with (x₁, y₁ ) = (- 6, 1) and (x₂, y₂ ) = (- 3, 2)
m = [tex]\frac{2-1}{-3+6}[/tex] = [tex]\frac{1}{3}[/tex] , then
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (- 3, 2) , then
2 = - 1 + c ⇒ c = 2 + 1 = 3
y = [tex]\frac{1}{3}[/tex] x + 3 ← equation of line
