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algol13
3 years ago
11

Write the equation of a line that is parallel to 3x+2y=10 and passes through the point (4,-5). Answer in slope-intercept form.

Mathematics
1 answer:
SCORPION-xisa [38]3 years ago
4 0

The equation of line is:

y = \frac{-3}{2}x+1

Further explanation:

The standard form of equation in point-slope form is:

y = mx+b

Given equation is:

3x+2y=10

We have to convert it into point slope form, for which we have to isolate y on one side of equation

3x+2y = 10\\2y = -3x +10\\y = \frac{-3}{2}x + \frac{10}{2}\\y = \frac{-3}{2}x + 5

Comparing with standard form:

m = -3/2

As the new line is parallel to given line, their slopes will be equal

So,

y = \frac{-3}{2}x+b

To find the value of b, putting the given point (4,-5) in equation

-5 = \frac{-3}{2}(4)+b\\-5 = -6+b\\b = -5+6 \\b = 1\\So\ the\ equation\ is:\\y = \frac{-3}{2}x+1

Keywords: Point-slope form, equation of line

Learn more about point-slope form of equation at:

  • brainly.com/question/1577690
  • brainly.com/question/1563227

#LearnwithBrainly

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Answer:

\large Q1:\ x=18\ ft\\\\Q2:\ 6\ inches

Step-by-step explanation:

Q3.

If ΔGHI and ΔJKL are similar, then the sides are in proportion:

\dfrac{JL}{GI}=\dfrac{LK}{IH}

We have

JL = x, GI = 9 ft, LK = 24 ft, IH = 12 ft.

Substitute:

\dfrac{x}{9}=\dfrac{24}{12}

\dfrac{x}{9}=2         <em> multiply both sides by 2</em>

x=18\ ft

Q4.

We must multiply the original length by a scale factor of 3/4:

\dfrac{3}{4}\cdot8\ in=\dfrac{3}{1}\cdot2\ in=(3)(2)\ in=6\ in

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9.v=39;w=59;x=121
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