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ASHA 777 [7]
3 years ago
10

Find an equation for the line with the given properties. Express your answer using either the general form or the​ slope-interce

pt form of the equation of a line. Parallel to the line ​; containing the point​ (0,0)
Mathematics
1 answer:
Vladimir [108]3 years ago
3 0

Answer:

y = 7x

Step-by-step explanation:

Complete question:

Find an equation for the line with the given properties. Parallel to the line 7x - y = -7; containing the point (0,0)

The equation of a line in point-slope form is expressed as;

y - y0 = m(x-x0)

(x0, y0) = (0,0)

Given the equation of the line as 7x - y = -7;

Rewrite and get the slope

-y = -7x - 7

y = 7x+7

Get the slope

mx = 7x

m = 7

Substitute into the equation

y - 0 = 7(x - 0)

y = 7x

Hence the required equation is y = 7x

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Answer:

\displaystyle y = \frac{t^2}{16} + 18

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Step-by-step explanation:

<u>Step 1: Define</u>

<em>Identify</em>

Point (0, 18)

\displaystyle \frac{dy}{dt} = \frac{1}{8} t

<u>Step 2: Find General Solution</u>

<em>Use integration</em>

  1. [Derivative] Rewrite:                                                                                         \displaystyle dy = \frac{1}{8} t\ dt
  2. [Equality Property] Integrate both sides:                                                        \displaystyle \int dy = \int {\frac{1}{8} t} \, dt
  3. [Left Integral] Integrate [Integration Rule - Reverse Power Rule]:                 \displaystyle y = \int {\frac{1}{8} t} \, dt
  4. [Right Integral] Rewrite [Integration Property - Multiplied Constant]:           \displaystyle y = \frac{1}{8}\int {t} \, dt
  5. [Right Integral] Integrate [Integration Rule - Reverse Power Rule]:              \displaystyle y = \frac{1}{8}(\frac{t^2}{2}) + C
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<u>Step 3: Find Particular Solution</u>

  1. Substitute in point [Function]:                                                                         \displaystyle 18 = \frac{0^2}{16} + C
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  3. Add:                                                                                                                   \displaystyle 18 = C
  4. Rewrite:                                                                                                             \displaystyle C = 18
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