Answer: A) y = 1/3x − 4
Step-by-step explanation:
Find the Equation Using Point-Slope Formula
slope: 1/3
point: (6, −2)
Use the slope 1 and a given point (6, −2) to substitute for [tex]x_1[/tex] and [tex]y_1[/tex] in the point-slope form
y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex]), which is derived from the slope equation m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
y − (−2) = 1/3 ⋅ (x − (6))
Simplify the equation and keep it in point-slope form.
y + 2 = 1/3 ⋅ (x − 6)
Solve for y.
1/3 ⋅ (x − 6).
Apply the distributive property.
y + 2 = 1
/3 x + 1
/3 ⋅ − 6
Combine 1/3 and x.
y + 2 = x/3 +1/3 ⋅ −6
Cancel the common factor of 3.
y + 2 = x
/3 − 2
Move all terms not containing y to the right side of the equation.
Subtract 2 from both sides of the equation.
y = x/3 − 2 − 2
Subtract 2 from −2. x
y = x/3 − 4
Reorder terms.
y = 1/3x − 4
List the equation in different forms.
Slope-intercept form:
y = 1/3x − 4
Point-slope form:
y + 2 = 1/3 ⋅ (x − 6)
