Write an equation of the line that passes through the point (2,3) with slope 3.

Mathematics

1 answer:

djyliett [7]3 years ago

5 0

Answer:

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

We have the slope m = 3, and the point (2, 3).

Put the value of slope and the coordinates of the given pint (x = 2, y = 3) to the equation of a line:

$3=3(2)+b$

$3=6+b$ subtract 3 from both sides

$-3=b\to b=-3$

Finally:

$y=3x-3$

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Here is an explanation if you want to know how to do it:

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The hardcover version of a book weighs 7 ounces while its paperback version weighs 5 ounces. Forty-five copies of the book weigh

konstantin123 [22]

Answer:

33 copies were paperback and 12 were hardcover.

Step-by-step explanation:

Let h represent the number of hardcover copies and p represent the number of paperback copies.

We know that the total number of copies was 45; this gives us the equation

h+p = 45

We know that each hardcover copy is 7 ounces; this gives us the expression 7h.

We also know that each paperback copy is 5 ounces; this gives us the expression 5p.

We know that the total weight was 249 ounces; this gives us the equation

7h+5p = 249

Together we have the system

$\left \{ {{h+p=45} \atop {7h+5p=249}} \right.$

We will use elimination to solve this. First we will make the coefficients of the variable p the same; to do this, we will multiply the top equation by 5:

$\left \{ {{5(h+p=45)} \atop {7h+5p=249}} \right. \\\\\left \{ {{5h+5p=225} \atop {7h+5p=249}} \right.$