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noname [10]
3 years ago
8

Draw a line through the point (2, 0) with a slope of 1/4

Mathematics
1 answer:
Nastasia [14]3 years ago
7 0

Answer:

y = 1/4 x - 1/2

Step-by-step explanation:

Remark

The general equation for a line is y = mx + b

You know that m = 1/4. The problem is what do you do about (2,0)?

Solution

y = 1/4 x + b                  Let x = 2 when y = 0

0 = 1/4 * 2 + b               multiply 2 * 1/4

0 = 1/2 + b                     Subtract 1/2 from both sides

b = - 1/2

equation y = 1/4 x - 1/2

Graph

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andriy [413]
Suppose that equation of parabola is
y =ax² + bx + c


Since parabola passes through the point (2,−15) then 
−15 = 4a + 2b + c

Since parabola passes through the point (-5,-29), then
−29 = 25a − 5b + c

Since parabola passes through the point (−3,−5), then 
−5 = 9a − 3b + c


Thus, we obtained following system:
4a + 2b + c = −15
25a − 5b + c = −29
9a − 3b + c = −5

Solving it we get that 
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Thus, equation of parabola is
y = −2x²− 4x + 1

____________________

Rewriting in the form of 
(x - h)² = 4p(y - k)

i) -2x² - 4x + 1 = y

ii) -3x² - 7x = y - 11
(-3x² and -7x are isolated)

iii) -3x² - 7x - 49/36 = y - 1 - 49/36
(Adding -49/36 to both sides to get perfect square on LHS)

iv) -3(x² + 7/3x + 49/36) = y - 3
(Taking out -3 common from LHS)

v) -3(x + 7/6)² = y - 445/36 

vi) (x + 7/6)² = -⅓(y - 445/36) 
(Shifting -⅓ to RHS)

vii) (x + 1)² = 4(-1/12)(y - 445/36)
(Rewriting in the form of 4(-1/12) ; This is 4p) 


So, after rewriting the equation would be - 

(x + 7/6)² = 4(-⅛)(y - 445/36)

__________________

I hope this is what you wanted.

Regards,
Divyanka♪
__________________
6 0
3 years ago
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poizon [28]

Answer:

Option 3

Step-by-step explanation:

3 × (-4 - n/-2) 《 5

5 is also included, so should be less than equal to 5

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