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3 years ago

What is the slope of the line

Mathematics

1 answer:

kicyunya [14]3 years ago

5 0

Answer:

-3

Step-by-step explanation:

Slope is rise over run or the change in y over change in x. So to find the slope count the difference from one point to the next, for example (0,4) and (1,1). In this case, the y-value decreases by 3, so -3, and the x-value increases by 1, so +1. Which would be -3/1 or just -3. One way to visually check is to remember that slopes less than -1 or greater than 1 make the line steeper and negative slopes make the graph decrease from left to right.

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Find the equation of a line that is perpendicular to y = 3x – 5 and passes through the point (1, -3).

Svetradugi [14.3K]

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

$\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \qquad y = \stackrel{\stackrel{m}{\downarrow }}{3}x-5$

well then therefore

$\stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{3\implies \cfrac{3}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{3}}}$

so we're really looking for the equation of a line with slope of -1/3 and that passes through (1, -3 )

$(\stackrel{x_1}{1}~,~\stackrel{y_1}{-3})\qquad \qquad \stackrel{slope}{m}\implies -\cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{-\cfrac{1}{3}}(x-\stackrel{x_1}{1})\implies y+3=-\cfrac{1}{3}x+\cfrac{1}{3} \\\\\\ y=-\cfrac{1}{3}x+\cfrac{1}{3}-3\implies y=-\cfrac{1}{3}x-\cfrac{8}{3}$

6 0

2 years 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.

4 0

3 years ago

Read 2 more answers

If you roll two fair dice repeatedly, what is the probability that you will get a sum of 4 before you get a sum of 5 ? (a) (b) (

AlexFokin [52]

Answer:

The probability that you will get a sum of 4 before you get a sum of 5 is $\frac{1}{12}$

Step-by-step explanation:

Given : If you roll two fair dice repeatedly.

To find : What is the probability that you will get a sum of 4 before you get a sum of 5 ?

Solution :

When two dice are rolled the outcomes are

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Total number of outcomes = 36

Favorable outcome get a sum of 4 before you get a sum of 5 is (1,3) ,(2,2) and (3,1) = 3

The probability that you will get a sum of 4 before you get a sum of 5 is

$P=\frac{3}{36}$

$P=\frac{1}{12}$

Therefore, The probability that you will get a sum of 4 before you get a sum of 5 is $\frac{1}{12}$

5 0

3 years ago

If y = kx, and x = 3 and y = 15, calculate k.

kenny6666 [7]

Answer:

k = 5

Step-by-step explanation:

Since the equation is y = kx and x equals 3 while y equals 15, in order to solve this equation we are going to have to substitute the variables with their answers:

x = 3

y = 15

15 = 3k

Now we divide 3 from both 3x and 15 to segregate the variable x:

15/3 = 3k/3

5 = k

Now to check our work we are going to substitute 5 for the variable k, 3 for the variable x and 15 for the variable y.

y = kx

15= (5)(3)

15 = 15

Tada, I hope this helps you!

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3 years ago

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AnnyKZ [126]

Answer:

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6 0

3 years ago

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