Select the two statements that are true about the equation y+6=−10(x−3).
the slope of the line is −10.
the slope of the line is 3.
one point on the line is (3, 6).
one point on the line is (3,−6)

The correct options are 1 and 4.

Step-by-step explanation:

The given equation of line is

                  .... (1)

The point slope form of a line is

              ..... (2)

Where m is the slope of line and (x₁,y₁) are points.

On comparing (1) and (2) we get

The slope of given line is -10 and the line passing through the points (3,-6).

Therefore correct options are 1 and 4.

2

∠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.