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denis23 [38]
4 years ago
10

A line passes through the point (–3, –4) and its y-intercept is (0, –9). What is the equation of the line that is parallel to th

e first line and passes through the point (3, –7)?
Mathematics
1 answer:
Goshia [24]4 years ago
5 0
Find the slope of this line
slope=(y2-y1)/(x2-x1)
slope=(-9-(-4))/(0-(-3))=(-9+4)/(3)=-5/3

yint is y=-9
y=mx+b
y=-5/3x-9

parllell means has same slope

y=-5/3x+b
find b by inputing point
(3,-7)
(x,y)
x=3
y=-7
-7=-5/3(3)+b
-7=-5+b
add 5
-2=b

the equation of the line is y=-5/3x-2
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Consider f(x) = b^. Which statement(s) are true for 0 &lt; b &lt; 1? Check all that apply.
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Answer:

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

<em>Consider f(x) = </em>b^{x}<em>. Which statement(s) are true for 0 < b < 1? Check all that apply.</em>

<em>The domain is all real numbers. </em>

<em>The domain is x > 0. </em>

<em>The range is all real numbers. </em>

<em>The range is y > 0. </em>

<em>The graph has x-intercept 1. </em>

<em>The graph has a y-intercept of 1. </em>

<em>The function is always increasing. </em>

<em>The function is always decreasing.</em>

My answer:

The domain is all real numbers.

True, the domain of a function is the complete set of possible values of the independent variable. Here, we can have unlimited values of x so we will have unlimited values of f(x)

<=> our domain (0 , +∞ )

The domain is x > 0.

Wrong, as we discussed in the aforementioned answer.

The range is all real numbers.

Wrong

The range is y > 0.

True, the range of a function is the complete set of all possible resulting values of the dependent variable (f(x), usually), after we have substituted the domain. Because this is an exponential function so:

<=> our range  (0 , +∞ )  or y>0

The graph has x-intercept 1.

we can set f(x)=0  and then we can solve for x

<em>f(x) = </em>b^{x}<em> = 0 </em>

x is undefined  so, x-intercept does not exist

The graph has a y-intercept of 1

y-intercept when x is 0, so f(x) = 1 . True.

The function is always decreasing

Because 0 < b < 1, The function is always decreasing when we increase the value of x.

So we choose A D F H

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3 years ago
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