What is the equation of the line that has a slope of 1/3 and goes through the point (6,−2)? A. y = 1/3x − 4
B. y = 1/3x + 4
C. y = 1/3x − 8
D. y = 1/3x

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  and  in the point-slope form  

y - = m(x - ), which is derived from the slope equation m =

  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)

answer: the answer is c.

step-by-step explanation:

she’s dividing 1/3 of the flour into 2 jars.

hope this : )

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.