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frozen [14]
3 years ago
6

Write the equation of a line that passes through the given point and is parallel to the given line.

Mathematics
1 answer:
monitta3 years ago
5 0

Answer:

  1. y=2x+5
  2. y= 1/3x -4

Step-by-step explanation:

1.

(1,-3)=(x_1,y_1)\\\\y =2x+2\\\\m = 2

Substitute values into point-slope form

y-y_1=m(x-x_1)\\\\y -3 =2(x-(-1))\\\\y-3=2(x+1)\\\\y-3=2x+2\\\\y=2x+2+3\\\\y=2x+5

2.

(18,2) =(x_1,y_1)\\\\3y-x=-12

Arrange equation in slope-intercept form (y=mx+b)and derive slope

3y =x-12\\\\\frac{3y}{3} =\frac{1x}{3} -\frac{12}{3} \\\\y = \frac{1}{3} x -4\\\\m = \frac{1}{3}

Substitute values into point-slope form

y-y_1=m(x-x_1)\\\\\\y-2=\frac{1}{3} (x-18)\\\\y-2=\frac{1}{3} x -6\\\\y=\frac{1}{3} x -6+2\\\\y=\frac{1}{3} x -4

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Help me I don’t understand it?
photoshop1234 [79]

let's do 1, 5, 6, 10 and 13.

1)

well, the denominator is the same on each, so we simply have to look at the numerator, who is larger 3 or 5?  3 < 5, 3 is less than 5, so then........\bf \cfrac{3}{12}

5)

\bf \begin{cases} \cfrac{2}{4}\implies \cfrac{1}{2} \\\\\\ \cfrac{10}{20}\implies \cfrac{1}{2} \end{cases}\qquad \implies \cfrac{2}{4}=\cfrac{10}{20}\implies \cfrac{1}{2}=\cfrac{1}{2}

6)

we can make both denominators the same if we simply <u>multiply each fraction by the other's denominator</u>.


\bf \begin{cases} \cfrac{1}{4}\cdot \cfrac{13}{13}\implies \cfrac{13}{52} \\\\\\ \cfrac{4}{13}\cdot \cfrac{4}{4}\implies \cfrac{16}{52} \end{cases}\qquad \implies \cfrac{13}{52}

10)

we'll convert the mixed fractions to improper fractions first, then make their denominator the same just like we did in 6).


\bf \stackrel{mixed}{4\frac{1}{7}}\implies \cfrac{4\cdot 7+1}{7}\implies \stackrel{improper}{\cfrac{29}{7}}~\hfill \stackrel{mixed}{3\frac{3}{18}}\implies \cfrac{3\cdot 18+3}{18}\implies \stackrel{improper}{\cfrac{57}{18}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} \cfrac{29}{7}\cdot \cfrac{18}{18}\implies \cfrac{522}{126} \\\\\\ \cfrac{57}{18}\cdot \cfrac{7}{7}\implies \cfrac{399}{126} \end{cases}\qquad \implies \cfrac{522}{126}>\cfrac{399}{126}\qquad therefore\qquad 4\frac{1}{7}>3\frac{3}{18}


13)

so both fractions are at a value from 9, so we can simply say, which is larger 2/6 or 4/12?


\bf \begin{cases} \cfrac{2}{6}\implies \cfrac{1}{3} \\\\\\ \cfrac{4}{12}\implies \cfrac{1}{3} \end{cases}\qquad \implies \cfrac{1}{3}=\cfrac{1}{3}\qquad therefore\qquad 9\frac{2}{6}=9\frac{4}{12}

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