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3 years ago

Which of the following lines has a slope of -1/3 and a y-intercept of 6? x - 3y = 6 x + 3y = 18 3y - x = 18

Mathematics

2 answers:

Blababa [14]3 years ago

4 0

Answer:

The correct option is 2. The equation of line is x + 3y = 18.

Step-by-step explanation:

The slope intercept form of a line is

$y=mx+b$

where, m is slope and b is y-intercept.

It is given that the slope of a line is -1/3 and a y-intercept is 6.

Substitute m=-1/3 and b=6 in the above equation.

$y=-\frac{1}{3}x+6$

Multiply both the sides by 3.

$3y=-x+18$

Add x on both the sides.

$x+3y=-x+18+x$

$x+3y=18$

The equation of line is x + 3y = 18. Therefore the correct option is 2.

erastovalidia [21]3 years ago

3 0

The second choice is correct, but I believe that either its +1/3 ( in the question) or -3y as that will give you the answer of: y=1/3x+6

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A car traveld 32 miles in 4 hours at this rate how many miles will the car travel in 0.5 hours

Mandarinka [93]

Answer:

4 miles

Step-by-step explanation:

In order to find how many miles the car will travel in 0.5 hours, we can set up a proportion.

$\frac{32}{4} = \frac{x}{0.5}$

We can now cross multiply to find the value of x.

$32 \cdot 0.5 = 16\\\\16\div4 = 4$

So the car can travel 4 miles in 0.5 hours.

Hope this helped!

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3 years ago

Read 2 more answers

If the sum of five consecutive odd integers is 95, what is the smallest of the five integers?

xxMikexx [17]

Answer:

15+ 17+ 19+ 21+23

Step-by-step explanation:

consecutive odd integers, like 1, 3, 5, 7

consecutive even integers, like 2, 4, 6, 8

an integer is a <em><u>whole number</u></em>

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3 years ago

A student created this table to represent a linear relationship between x and y.X Y-2. 10.0-1. 7.50. 5.01. 2.52. 0The student sa

alex41 [277]

The relationship between x and y is represent as:

Since, the relationship is linear.

The standard form of equation of line is:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Consider any two set x and y values from the given relationship.

Let (-2, 10) and (-1,7.5)

$\text{Substitute x}_1=-2,y_1=10,x_2=-1,y_2=7.5\text{ in the standard equation of line.}$

$\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-10=\frac{7.5-10}{-1-(-2)}(x-(-2)) \\ y-10=\frac{-2.5}{1}(x+2) \\ y-10=-2.5(x+2) \\ y=-2.5(x+2)+10 \end{gathered}$

The equation of the linear relationship between x and y is:

y = -2.5(x + 2) + 10

Now, to check that the point (9, -17.5) lies on the represented relationship between x and y

Substitute x = 9 and y = -17.5 in the equation y = -2.5(x + 2) + 10

y = -2.5(x + 2) + 10

-17.5 = -2.5(9 + 2) + 10

-17.5 = -2.5(11) + 10

-17.5 = -27.5 + 10

-17.5 = -17.5

Thus, LHS = RHS

Hence the point (9, -17.5) lie on the given linear relationship between x and y.

Answer: The point (9, -17.5) lie on the given linear relationship between x and y.

8 0

1 year ago

Find the angles, θ<0<360, that satisfy the equation below, to the nearest 10th of a degree.

podryga [215]

Answer:

$\cos( \theta) = \frac{ - \sqrt{} 7}{5} \\ \theta = \cos {}^{ - 1} ( \frac{ \sqrt{} - 7}{5} ) \\ \theta = 58.1 \degree, \: 121.9 \degree, \: 238.1 \degree$

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2 years ago

[Systems of equations] (/20) 1. Suppose the coefficient matrix of a system of linear equations has a pivot position in every row

Marina86 [1]

Answer:

The system is consistent because the rightmost column of the augmented matrix is not a pivot column.

Step-by-step explanation:

It is given that the coefficient of the matrix of a linear equation has a pivot position in every row.

It is provided by the Existence and Uniqueness theorem that linear system is said to be consistent when only the column in the rightmost of the matrix which is augmented is not a pivot column.

When the linear system is considered consistent, then every solution set consists of either unique solution where there will be no any variables which are free or infinitely many solutions, when there is at least one free variable. This explains why the system is consistent.

For any m x n augmented matrix of any system, if its co-efficient matrix has a pivot position in every row, then there will never be a row of the form [0 .... 0 b].

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3 years ago