Write an equation of the line passing through point P(0, −1)P(0, −1) that is parallel to the line y = −2x+3y = −2x+3.

Parallel lines have the same slope

The equation of the line is:

The equation is given as:

The slope intercept equation of a line is:

Where

slope

By comparison

From the question, we understand that the line is parallel to

This means that they have the same slope,

The equation of the line is then calculated using:

This gives

Open bracket

Hence, the equation of the line is:

See attachment for the graph of both lines

Read more about equations of parallel lines at:

link

y = - 2x - 1

Step-by-step explanation:

Assuming the line has equation y = - 2x + 3

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x + 3 ← is in slope- intercept form

with slope m = - 2

Parallel lines have equal slopes, thus

y = - 2x + c ← is the partial equation

Note the line passes through (0, - 1) ⇒ c = - 1

y = - 2x - 1 ← equation of parallel line

∠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.