Write an equation in point-slope form and slope-intercept form for the line that passes through (8, 1) and (-2,9).

point-slope form: y - 1 = -4/5(x - 8)    

slope-intercept form:  y = -4/5x + 7.4

Step-by-step explanation:

Find slope using the points (8, 1) and (-2, 9):

  m = (y₂ - y₁) / (x₂ - x₁)

      = (9 - 1) / (-2 - 8)

      = 8 / -10

  m = -4/5

Find y-intercept using slope m from above and anyone of the given points, let's use (8, 1):

  y = mx + b

  1 = -4/5(8) + b

  1 = -6.4 + b

   b = 7.4

Use slope m and y-intercept b above to form equation of line in slope-intercept form:

  y = mx + b

  y = -4/5x + 7.4

For point slope form use slope m from above and a point, again let's use (8, 1):

  y - y₁ = m(x - x₁)

  y - 1 = -4/5(x - 8)    

∠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.

step-by-step explanation:

mean or average is 40.6