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marishachu [46]
2 years ago
10

A line passes through the point (-6,-9) and has a slope of 5/2.

Mathematics
2 answers:
mezya [45]2 years ago
8 0

(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-9})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-9)}=\stackrel{m}{\cfrac{5}{2}}(x-\stackrel{x_1}{(-6)})\implies y+9=\cfrac{5}{2}(x+6) \\\\\\ y+9=\cfrac{5}{2}x+15\implies y=\cfrac{5}{2}x+6

NISA [10]2 years ago
6 0

Answer:

  y = 5/2x +6

Step-by-step explanation:

The slope-intercept form of the equation of a line is ...

  y = mx +b . . . . line with slope m and y-intercept b

__

The above equation can be solved for b to give ...

  b = y -mx

Using the given values m = 5/2 and (x, y) = (-6, -9), we find b to be ...

  b = -9 -(5/2)(-6) = -9 +15 = +6

Then the slope-intercept equation is ...

  y = 5/2x +6

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3 years ago
arthur wants to buy an item that costs p dollars before tax. using a 6% sales tax rate, write two different expressions that rep
Mkey [24]

For this case we have the following variable:

p: cost of the item that Arthur wants to buy before tax

The expression for the 6% tax is given by:

\frac{6}{100} p

Or equivalently:

0.06p

Therefore, two different expressions for the total cost are:

Expression 1:

p + \frac{6}{100} p

Expression 2:

p + 0.06p

To prove that they are equal, suppose that the item costs $ 100:

Expression 1:

p + \frac{6}{100} p

100+ \frac{6}{100} 100

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106

Expression 2:

p + 0.06p

100 + 0.06 (100)

100 + 6

106

Since the cost is the same, then the expressions are the same.

Answer:

Two different expressions that model the problem are:

p + \frac{6}{100} p

p + 0.06p

8 0
3 years ago
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