Write the equation of the line that passes through (1, 3) and has a slope of 2 in point-slope form. (2 points) y − 1 = 2(x − 3) y − 3 = 2(x − 1) x − 1 = 2(y − 3) x − 3 = 2(y − 1).

  y − 3 = 2(x − 1)

Step-by-step explanation:

The point-slope form of the equation of a line with slope m through point (h, k) is ...

  y -k = m(x -h)

You have m=2, h=1, k=3, so the equation is ...

  y -3 = 2(x -1)

∠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.

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