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2 years ago

Write an equation of the line that passes through (18, 2) and is parallel to the line 3y−x=−12

Mathematics

1 answer:

miskamm [114]2 years ago

3 0

keeping in mind that parallel lines have the same exact slope, hmmmm what's the slope of the line above anyway?

$\bf 3y-x=-12\implies 3y=x-12\implies y=\cfrac{x-12}{3}\implies y = \cfrac{x}{3}-\cfrac{12}{3} \\\\\\ y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{3}}x-4\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

so we're really looking for the equation of a line whose slope is 1/3 and runs through (18,2)

$\bf (\stackrel{x_1}{18}~,~\stackrel{y_1}{2})~\hspace{10em} \stackrel{slope}{m}\implies \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{\cfrac{1}{3}}(x-\stackrel{x_1}{18}) \\\\\\ y-2=\cfrac{1}{3}x-6\implies y=\cfrac{1}{3}x-4$

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olchik [2.2K]

Answer:

x + 5y = 0

Step-by-step explanation:

y = mx + b

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1 = -1/5 (-5) + b

1 = 1 + b

b = 0

y = -1/5 x

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2 years ago

5+4 X 2+6-2 X 2-1

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A man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. He puts twice as muc

Masteriza [31]

Let x represent amount invested in the higher-yielding account.

We have been given that a man puts twice as much in the lower-yielding account because it is less risky. So amount invested in the lower-yielding account would be $2x$ .

We are also told that his annual interest is $6600 dollars. We know that annual interest for one year will be principal amount times interest rate.

$I=Prt$ , where,

I = Amount of interest,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

We are told that interest rates are 6% and 10%.

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$10\%=\frac{10}{100}=0.10$

Amount of interest earned from lower-yielding account: $2x(0.06)=0.12x$ .

Amount of interest earned from higher-yielding account: $x(0.10)=0.10x$ .

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Let us solve for x.

$0.22x=6600$

$\frac{0.22x}{0.22}=\frac{6600}{0.22}$

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Therefore, the man invested $30,000 at 10%.

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Therefore, the man invested $60,000 at 6%.

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You are considering a 5/1 ARM. What does the 5 represent?

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2 years ago

Read 2 more answers

In the diagram, the measurements that are labeled are known, while the other measurements are unknown. Which measurement of acut

andrew-mc [135]

As the sine rule states,

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3 years ago