enmobladatn
2022-07-31
Answered

I have to find the slope and the y-intercept of 3x+7=0

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Danica Ray

Answered 2022-08-01
Author has **15** answers

For this question, let's isolate for x alone by subtracting 7 fromboth sides of the equation to get:

3x = -7

Now, divide both sides by 3 to isolate for the variable x alone toget:

$x=\frac{-7}{3}$

At this point, we have an equation, however, notice that y simplydoes not appear here. In fact, it never appeared in the original questionwhich means that y takes upon all values of this value of x.

Now, equations where x = a number, have graphs where we have avertical line at the x value going straight up and straight down[since it doesn't matter which y-value we hit].

Therefore, there is no y-interceptand no slope for this particular equation!

3x = -7

Now, divide both sides by 3 to isolate for the variable x alone toget:

$x=\frac{-7}{3}$

At this point, we have an equation, however, notice that y simplydoes not appear here. In fact, it never appeared in the original questionwhich means that y takes upon all values of this value of x.

Now, equations where x = a number, have graphs where we have avertical line at the x value going straight up and straight down[since it doesn't matter which y-value we hit].

Therefore, there is no y-interceptand no slope for this particular equation!

Deborah Wyatt

Answered 2022-08-02
Author has **4** answers

3x+7=0

3x+7=y

slope: because of 3x->

slope equal 3

y-int, let x=0

3(0)+7=y

y=7

y-intercept=7

3x+7=y

slope: because of 3x->

slope equal 3

y-int, let x=0

3(0)+7=y

y=7

y-intercept=7

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Question about changing a logarithm's base

I've been using the following method to derive/remember the logarithm base conversion formula: If I want to convert${\mathrm{log}}_{a}\left(x\right)$ to an expression in base b, I say,

${a}^{{\mathrm{log}}_{a}\left(x\right)}=x$

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$\mathrm{log}}_{a}\left(x\right)=\frac{{\mathrm{log}}_{b}\left(x\right)}{{\mathrm{log}}_{b}\left(a\right)$

It kind of feels like I'm working backwards, and I was wondering if there's a more direct way to go about it. I tried:

${\mathrm{log}}_{a}\left(x\right)={\mathrm{log}}_{a}\left({b}^{{\mathrm{log}}_{b}\left(x\right)}\right)$

${\mathrm{log}}_{a}\left(x\right)={\mathrm{log}}_{b}\left(x\right){\mathrm{log}}_{a}\left(b\right)$

but couldn't rid myself of the loga in the right-hand side of the equation. It occurred to me that if I could rewrite the "a" subscript as "$b}^{\mathrm{log}b\left(a\right)$ ", I might be onto something. (Or might not.) Does the notation ever get used like that, where you perform a substitution in a subscript?

I've been using the following method to derive/remember the logarithm base conversion formula: If I want to convert

It kind of feels like I'm working backwards, and I was wondering if there's a more direct way to go about it. I tried:

but couldn't rid myself of the loga in the right-hand side of the equation. It occurred to me that if I could rewrite the "a" subscript as "