Which is the equation of a line that is parallel to the line represented by y=3/4x-1/2?

3rd option (

Step-by-step explanation:

Two lines are said to be parallel of they have same slope.

For a line written in the standard form:

m represents the slope while q is the y-intercept.

The line mentioned in the text of the problem is

so it has slope of . Therefore we have two find the line with the same slope among the options given.

Looking at the options given, we see that the third line:

has the same slope (3/4), therefore it is the correct choice.

∠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.

it is 10.6 according to my calculations