Write the equation of the line that goes through points (9, 1) and (-1, 6) in slope-intercept form. (hint: find slope first and then use y = mx + b).

First things first, you need to find the gradient which is:

Take (9 , 1) , 9 = x₁ and 1 = y₁

Also means that in ( -1, 6 ) , -1 = x₂ and 6 = y₂

Simply plug these values into the formula:

Which simplifies to:

Which then also simplifies down to:

So the gradient is , so mx - x

Now plug this into y = mx + b with one point, such as ( 9 , 1) where 1 is y and x is 9:

1 = ( x 9) + b

Which means that this can be rearranged to make 'b' the subject, making sure the positive negative half is made positive:

1 + 4.5 = b

So the intercept is b

This would then make the y = mx + b:

∠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.