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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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Now, use substitution to solve this. I will isolate s from this equation so the new equation should be s=-a+7. Plug in this equation to the other equation, it will look like this 9.10a+7.75(-a+7)=56.95. Simplify this to get 9.10a-7.75a+54.25=56.95. Simplify this again and the equation will become 1.35a=2.70. Then divide 1.35 by each side to get a=2. This Mrs. Williams bought two adult tickets. Plug in 2 into a+s=7, it will look like this (2)+s=7. Simplify this and get s=5. This means Mrs. Williams bought five adult tickets. Therefore she bought 2 adult tickets and 5 student tickets.

Hope this helps

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