Mathematics, 25.02.2021 19:40 coolmonkey3643

With slope –1/4, passing through (-4, -1)

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Answer from: qloc

$y = -\frac{1}{4}x - 2$

Step-by-step explanation:

i'm not sure if you're trying to find the equation of the line ?? but i'll assume that's the case and find the slope-intercept form equation of the line.

slope intercept form is y = mx + b , where is the slope and is the y-intercept. since the slope is already identified, you can plug in $-\frac{1}{4}$ for .

⇒ $y = -\frac{1}{4}x+b$

plug in the and values from the coordinate pair that passes through the line, which is (-4, -1). you can start with either or , but i'm going to start with .

first, plug in for .

$y = -\frac{1}{4}x+b$ ⇒ $y = -\frac{1}{4}(-4)+b$

now plug in for .

$y = -\frac{1}{4}(-4)+b$ ⇒ $-1 = -\frac{1}{4}(-4)+b$

after plugging in all of the given values, the equation is now $-1 = -\frac{1}{4}(-4)+b$ , in which you need to solve for .

now it's time to solve! begin by multiplying $-\frac{1}{4}(-4)$ in order to simplify the right side of the equation.

$-\frac{1}{4}(-4) = 1$

you now have -1 = 1 + b . subtract 1 from both sides of the equation. on the right side, it cancels itself out, leaving you with . on the left side of the equation, you now have -1 - 1 , which equals .

therefore -2 = b , or b = -2 .

now that you've solved for your value, plug it into your initial slope-intercept form equation!

$y = -\frac{1}{4}x + b$ ⇒ $y = -\frac{1}{4}x - 2$

if you want to check to make sure that the values are correct, plug (-4, -1) into your completed slope-intercept form equation. as you did in the beginning, plug in for and for .

$y = -\frac{1}{4}x - 2$ ⇒ $-1 = -\frac{1}{4}(-4) - 2$

begin simplifying by multiplying $-\frac{1}{4}(-4)$ .

$-1 = -\frac{1}{4}(-4) - 2$ ⇒ -1 = 1 - 2

subtract 1 - 2 .

⇒

since both sides of the equation are equal, that means your value of is correct because it makes the equation true!

aaaand there you go! i hope this helps. have a great day! <3

Answer from: Quest

∠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.

Answer from: Quest

351°f

step-by-step explanation:

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