If m = 6 , and ( x , y ) = ( − 1 , − 3 ) , solve y = m x + b for b .

Mathematics

1 answer:

Leya [2.2K]2 years ago

6 0

-3= 6(-1) + b
-3= -6+b
3=b
B is 3

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What is the equation of a line parallel to y=1/2×+6 that passes through (-4,1)

IgorC [24]

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

$y = \stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{2}}x+6\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

so we're really looking for the equation of a line whose slope is 1/2 and passes through (-4 , 1)

$(\stackrel{x_1}{-4}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{(-4)}) \\\\\\ y-1=\cfrac{1}{2}(x+4)\implies y-1=\cfrac{1}{2}x+2\implies y=\cfrac{1}{2}x+3$

5 0

1 year ago

What is the probability that a marble chosen at random is

Brums [2.3K]

Answer:

$P=\frac{6}{11}$

Step-by-step explanation:

The probability can be defined as the ratio between the possible events and the total number of outcomes.

In this case, according to the image attached, the total number of outcomes is 11, because they are 11 marbles in total.

Now, the specific event is all shaded marbles or labeled with a multiple of 3. With this specific characteristics 6 marbles, because there are 5 shaded marbles and 6 is a multiple of 3. So, the possible events are 6.

Therefore, the probability is

$P=\frac{6}{11}$

The right answer is the last choice.