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Alja [10]
3 years ago
13

Write the equation of the line given two points (5, 6) (4, 8). Write the answer in point-slope form.

Mathematics
1 answer:
Lady_Fox [76]3 years ago
3 0

Answer:

see explanation

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

To calculate m use the slope formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (5, 6) and (x₂, y₂ ) = (4, 8)

m = \frac{8-6}{4-5} = \frac{2}{-1} = - 2

There are 2 possible equations, however both are equivalent

Using (a, b) = (5, 6), then

y - 6 = - 2(x - 5)

Using (a, b) = (4, 8), then

y - 8 = - 2(x - 4)

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<em>Question:</em>

<em>If one basket contains five bottles each weighing 7 1/4 and the other basket has six apples each weighing 6 1/2 ounces. Which basket is heavier and by how much ?</em>

Answer:

The basket of bottles weighs more than the basket of apples by 3\frac{3}{4} ounces

Step-by-step explanation:

Given

Bottles = 5

Weight(Bottle) = 7\frac{1}{4}

Apples = 6

Weight(Apple) = 6\frac{1}{2}

Required

Determine which basket is heavy

and by how much?

First, we need the total weight of each basket.

For the bottles' basket

Total\ Weight = Weight * Bottles

Total\ Weight = 7\frac{1}{4} * 5

Total\ Weight = \frac{29}{4} * 5

Total\ Weight = \frac{29 * 5}{4}

Total\ Weight = \frac{145}{4}

Total\ Weight = 36\frac{1}{4}

For the bottles' basket

Total\ Weight = Weight * Apples

Total\ Weight = 6\frac{1}{2} * 5

Total\ Weight = \frac{13}{2} * 5

Total\ Weight = \frac{13* 5}{2}

Total\ Weight = \frac{65}{2}

Total\ Weight = 32\frac{1}{2}

By comparing both total weights, 36\frac{1}{4} > 32\frac{1}{2}

Hence:

The basket of bottles weighs more than the basket of apples

Calculating the difference:

Difference = 36\frac{1}{4} - 32\frac{1}{2}

Difference = \frac{145}{4} - \frac{65}{2}

Difference = \frac{145 - 130}{4}

Difference = \frac{15}{4}

Difference = 3\frac{3}{4}

Hence:

It weighs more by 3\frac{3}{4} ounces

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