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Serga [27]
3 years ago
10

Exercise 21.2

Mathematics
1 answer:
m_a_m_a [10]3 years ago
4 0

Answer:

1.y=3x+1

2.y=1/3x+2

3.y=-2x+5

4.y=4x

5.y=4x-4

6.y=-2x-5

Step-by-step explanation:

(i)

y=mx+c

10=(m)3+1

10=3m+1

10-1=3m

m =3

y=3x+1

And so on...

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Write an absolute value equation for the graph shown below
BabaBlast [244]
So, hmmm keeping in mind that, an absolute value expression is in effect a piece-wise function, let's find its "slopes", the negarive slope on the left-side and the positive slope on the right side, and let's use the vertex point as our first point

what is the slope of a line that passes through (2, -1) and (0,7)

\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%   (a,b)
&({{ 2}}\quad ,&{{ -1}})\quad 
%   (c,d)
&({{ 0}}\quad ,&{{ 7}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{7-(-1)}{0-2}\implies \cfrac{7+1}{-2}\implies -4
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-1)=-4(x-2)
\\\\\\
\boxed{y+1=-4(x-2)}

now, what is the slope of a line that passes through (2, -1) and (4,7)

\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%   (a,b)
&({{ 2}}\quad ,&{{ -1}})\quad 
%   (c,d)
&({{ 4}}\quad ,&{{ 7}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{7-(-1)}{4-2}\implies \cfrac{7+1}{2}\implies 4
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-1)=4(x-2)
\\\\\\
\boxed{y+1=4(x-2)}

since an absolute value expression is just a piece-wise with a +/- versions, then we can just combine those two.

\bf \begin{cases}
y+1=-4(x-2)\\
y+1=4(x-2)
\end{cases}\implies y+1=\pm 4(x-2)
\\\\\\
y+1=|4(x-2)|\implies y=|4(x-2)|-1
7 0
3 years ago
Apply the distributive property to create an equivalent expression.<br> 6(3c - 5d + 6) =6(3c−5d+6)=
Mars2501 [29]

Answer:

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Step-by-step explanation:

6(3c - 5d + 6)

6 × 3c = 18c

6 × -5d = -30d

6 × 6 = 36

8 0
3 years ago
Read 2 more answers
What is the sum of 12 – 5i and –3 + 4i?
8090 [49]
12 - 3 =9 and -5i+4i=1i or i so it is      {9-i}
6 0
3 years ago
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I need help with math
marin [14]
What math are you talking about. I don't see anything.
7 0
4 years ago
Can someone please help me with this
Murljashka [212]
The answer is:  [C]:  "  2/3, 6/9, 8/12 " .
____________________________________________
4 0
4 years ago
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