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kow [346]
3 years ago
11

Give the equation of the line that is parallel to y=-3x+1 and goes through (-5,-6)

Mathematics
1 answer:
stich3 [128]3 years ago
8 0

Hi there! The answer is y = -3x - 21

Let's set up the equation of the line step by step! First we need to know that we need to set up an equation in slope-intercept form. We get the following:

y = ax + b.
a represents the slope of the line.
b represents the intercept with the y-axis.

Since our new line is parallel to y = -3x + 1, both lines have the same slope. Therefore the slope of our line, which is represented by a, is -3.

y = -3x + b.
We also know that this line goes through the point (-5, -6) and therefore we can plug in these coordinates into our formula.

-6 = -3 × -5 + b
Simplify

-6 = 15 + b
Subtract 15

-21 = b
Switch sides

b = -21
Hence, y = -3x - 21

~ Hope this helps you!
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The graph of y=ax^2+bx+c passes through points (0,5), (1,10), and (2,19). Find a+b+c.
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Answer:   a = 2   b = 3   c = 5  

Literally a+ b+c = 10, but I don't think that's what the question means to ask.

the equation is 2x² +3x + 5

Step-by-step explanation:   Substitute the values of the given coordinates into the formula and use algebra (solve a system of equations by substitution and elimination) to get the values  of a,b & c

y=ax²+bx+c    using  (0,5), (1,10), and (2,19)

5=a(0)²+b(0)+c   becomes 5= 0+0 + c .so we find c = 5

10=a(1)²+b(1)+c    becomes 10 = a + b + c

19=a(2)²+b(2)+c .  becomes 19 = 4a + 2b + c

Substitute the 5 for c.  Then rewrite

10 = a + b + 5      becomes     5 = a+ b     to eliminate b multiply this be (-2)

(-2)( 5 = a+ b) .to get -10 = -2a - 2b  

19 = 4a + 2b + 5  becomes   14 = 4a + 2b  

_______________  Add these two

14 = 4a + 2b

<u>-10 = -2a - 2b</u><u> </u>    this will eliminate the "b" term

4 = 2a       divide both sides by 2   so you have   a = 2  

substitute in 10=a(1)²+b(1)+5 to find b

10=2(1)²+b(1)+5 .becomes  5 = 2 + b   Subtract 2 from both sides

b = 3

So now you have all three values:  

a = 2  b= 3  c = 5  

I am attaching the graph. I hope this deserves Brainiest.

Best wishes in your studies!

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Answer:

Step-by-step explanation:

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