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
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (5, 6) and (x₂, y₂ ) = (- 1, 4)
m = [tex]\frac{4-6}{-1-5}[/tex] = [tex]\frac{-2}{-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 (- 1, 4 ) , then
4 = - [tex]\frac{1}{3}[/tex] + c ⇒ c = [tex]\frac{12}{3}[/tex] + [tex]\frac{1}{3}[/tex] = [tex]\frac{13}{3}[/tex]
y = [tex]\frac{1}{3}[/tex] x + [tex]\frac{13}{3}[/tex] ← equation of line
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The equation of a line in point- slope form is
y - b = m(x - a)
m is the slope and (a, b) a point on the line
Here m = 3 and (a, b) = (- 2, 0 ) , then
y - 0 = 3(x - (- 2) ) , that is
y = 3(x + 2)
y = 3x + 6 ← equation of line
