Write the equation of each line using the given information.
a. the points (-4,1) and (2, 4) both lie on the line
b. m = -1 and the point (2, -1) lies on the line.
c. it has the same slope as y = 5 and passes through (1,1).
d. m = -3 and it has a y-intercept of (0,8).

See explanation.

Step-by-step explanation:

We need a point and a slope to have a point slope equation.

We need a slope and y-intercept to write in slope intercept form.

A) or

B)

C)

D)

∠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.