We are asked to write the equation of the line in slope-intercept form ($y=mx+b$) for the given problems. We have to determine the slope $m$ and y-intercept $b$ from tables, graphs, and word problems.

1. Problem Description

We are asked to write the equation of the line in slope-intercept form ($y=mx+b$) for the given problems. We have to determine the slope $m$ and y-intercept $b$ from tables, graphs, and word problems.

2. Solution Steps

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1. The table shows the number of pieces of art and their cost.

When the number of pieces of art is 0, the cost is

3

0. This means the y-intercept is

3

0. So, $b=30$.

We can find the slope $m$ using two points from the table, say (2, 90) and (4, 150).

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{150 - 90}{4 - 2} = \frac{60}{2} = 30$

So, $m=30$.

The equation is $y = 30x + 30$.

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2. The table shows the time (in minutes) and the distance (in meters).

We can find the slope $m$ using two points from the table, say (5, 1930) and (10, 1880).

$m = \frac{1880 - 1930}{10 - 5} = \frac{-50}{5} = -10$

So, $m = -10$.

To find the y-intercept $b$, we can use the point-slope form:

$y - y_1 = m(x - x_1)$

$y - 1930 = -10(x - 5)$

$y - 1930 = -10x + 50$

$y = -10x + 1980$

So, $b = 1980$.

The equation is $y = -10x + 1980$.

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3. The graph passes through the origin, so it has the coordinate (0, 0).

The line also appears to pass through the point (1, 2). Therefore the slope is given as

$m = \frac{2-0}{1-0} = 2$.

The y-intercept is $b = 0$.

The equation is $y = 2x$.

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4. From the graph, we can identify two points: (1, 28) and (3, 44).

The slope is $m = \frac{44 - 28}{3 - 1} = \frac{16}{2} = 8$.

So, $m = 8$.

Using the point-slope form with (1, 28):

$y - 28 = 8(x - 1)$

$y - 28 = 8x - 8$

$y = 8x + 20$

The y-intercept is $b = 20$.

The equation is $y = 8x + 20$.

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5. You make $50 for signing up to sell tickets. You also make $0.75 for each ticket you sell.

Let $y$ be the total amount you make, and $x$ be the number of tickets you sell.

The slope is $0.75$ and the y-intercept is $50$.

The equation is $y = 0.75x + 50$.

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6. Coral Snorkeling charges $25 to rent equipment and $30 per hour of boat rental.

Let $y$ be the total cost, and $x$ be the number of hours of boat rental.

The slope is $30$ and the y-intercept is $25$.

The equation is $y = 30x + 25$.

3. Final Answer

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1. $y = 30x + 30$

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2. $y = -10x + 1980$

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3. $y = 2x$

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4. $y = 8x + 20$

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5. $y = 0.75x + 50$

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6. $y = 30x + 25$