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guapka [62]
4 years ago
11

Write each equation in standard form

Mathematics
1 answer:
Lunna [17]4 years ago
4 0

Standard form = Ax + By = c

a.

y + 1 = x

<em><u>Subtract 1 from both sides.</u></em>

y = x - 1

<em><u>Subtract x from both sides.</u></em>

-x + y = 1

b.

2y = -6 + 2x

<em><u>Subtract 2x from both sides.</u></em>

-2x + 2y = -6

c.

2x + 4y = -3

This equation is already in standard form.

d.

-12x - 9 = -6y

<em><u>Add 6y to both sides.</u></em>

-12x + 6y - 9

<em><u>Add 9 to both sides.</u></em>

-12x + 6y = 9

e.

-2y - 4 = -3x

<em><u>Add 3x to both sides.</u></em>

3x -2y - 4

<em><u>Add 4 to both sides.</u></em>

3x - 2y = 4

f.

-4y = 10

Because there is no x value, nothing more needs to be done to this equation.

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The graph is attached.

We first graph the point where his catch reached the surface, (35, 0).  Since it travels upward at a constant rate, the graph will be linear.  We also need to know where it starts (what depth it is at when he begins reeling it in).  We can use the formula d=rt as a template for our function.  d would be distance (in our case, depth), r is the rate (speed) and t is the amount of time.

To find how far the catch had to travel to reach the surface, we set up our equation as:
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Lesechka [4]

There's not much math work here, they just want you to eyeball the graph and give the closest grid point to where the two lines meet.

Let's translate the question.

Solution to the system

That's the x and y values where the two lines cross.  That's because the meeting point is the value of x and y that satisfies both equations.

Approximation ... to the nearest integer values

Where two integer grid lines cross is called a lattice point.  It's a point with integer coordinates.  Our solution, the meet of these two lines, doesn't fall exactly on a lattice point.  The nearest integer values means the closest lattice point to our intersection of lines.

Eyeballing the graph, I'd say (x,y)=(2,3) is the closest point.

Answer: (2,3)   second choice

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