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Anastaziya [24]
3 years ago
8

What is the equation of this line in standard form? (Please explain)

Mathematics
1 answer:
Lady bird [3.3K]3 years ago
3 0

\bf (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{\frac{1}{2}}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-(-1)}{\frac{1}{2}-(-3)}\implies \cfrac{2+1}{\frac{1}{2}+3} \\\\\\ \cfrac{3}{~~\frac{7}{2}~~}\implies \cfrac{3}{1}\cdot \cfrac{2}{7}\implies \cfrac{6}{7}


\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-1)=\cfrac{6}{7}[x-(-3)] \\\\\\ y+1=\cfrac{6}{7}(x+3)\implies y+1=\cfrac{6}{7}x+\cfrac{18}{7}\implies y=\cfrac{6}{7}x+\cfrac{18}{7}-1 \\\\\\ y=\cfrac{6}{7}x+\cfrac{11}{7}


now, let's bear in mind that

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

so, let's multiply both sides by the LCD of all fractions, in this case that'd be 7, to do away with the denominators.


\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{7}}{7(y)=7\left( \cfrac{6}{7}x+\cfrac{11}{7} \right)}\implies 7y=6x+11\implies -6x+7y=11 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 6x-7y=-11~\hfill

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<u>Solution-</u>

Let's assume, the rate of interest of $8000 is x%,

then the rate of interest of $17000 is (x+0.3x) =1.3x%

Interest earned by $8000,

i_1=\frac{8000\times x\times 1}{100} =80x

Interest earned by $17,000,

i_2=\frac{17000\times 1.3x\times 1}{100} =221x

According to the question,

\Rightarrow i_1=i_2+276

\Rightarrow 221x=80x+276

\Rightarrow 221x-80x=276

\Rightarrow 141x=276

\Rightarrow x=1.96

∴ Rate of interest of $8000 is 1.96% and rate of interest of $17000 is (1.3×1.96) =2.55%

3 0
3 years ago
Solve −x+5≤4 or 2x+3≥−1 and write the solution in interval notation.
serg [7]

Answer:

Step-by-step explanation:

\left \{ {{-x+5\leq 4} \atop {2x+3\geq -1}} \right.   ⇒ x\geq 1\\2x\geq 4\\x\geq -2

or

x \geq -2\\(-2,+ { \infty} ) (Answer)

6 0
2 years ago
I attached the math problem below and I hope u guys help me. Thxs to who's gonna answer!
vova2212 [387]

Answer:

Numbers | least to greatest | opposites | opposites least to greatest

1/4, -1/2    | -1/2, 1/4                | -1/4, 1/2     | -1/4, 1/2

2, -10        | -10, 2                   | -2, 10         | -2, 10

0, 3 1/2     | 0, 3 1/2                | 0, -3 1/2    | -3 1/2, 0

-5, -5.6     | -5.6, -5                 | 5, 5.6       | 5, 5.6

24 1/2, 24 | 24, 24 1/2            | -24 1/2 -24 | -24 1/2 -24

-99.9, -100 | -100, -99.9         | 99.9, 100 | 99.9, 100

-0.05, -0.5  | -0.5, -0.05         | 0.5, 0.05 | 0.05, 0.5

-0.7, 0       | -0.7, 0                  | 0.7, 0       | 0, 0.7

100.02, 100.04 | 100.02, 100.04 | -100.02, -100.04 | -100.04, -100.02

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8 0
3 years ago
draw a line representing the rise and a line representing the run of the line. State the slope of the line in simplest form
agasfer [191]

Answer:

m = -1

Step-by-step explanation:

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m = Δy/Δx

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4 0
3 years ago
Do u agree?I m not pretty sure
nika2105 [10]
It looks correct to me :)
6 0
3 years ago
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