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3 years ago

Find the equation of a line passing through the point (1, 1) and having a slope of 3.

Mathematics

1 answer:

maks197457 [2]3 years ago

5 0

Given:

The equation of the line passes through the point (1,1) and having a slope of 3.

We need to determine the equation of the line.

Equation of the line:

The equation of the line can be determined using the formula,

$y-y_1=m(x-x_1)$

Substituting the point (1,1) and the slope m = 3 in the above formula, we get;

$y-1=3(x-1)$

Simplifying the terms, we get;

$y-1=3x-3$

Adding both sides of the equation by 1, we get;

$y=3x-2$

Thus, the equation of the line is $y=3x-2$

Hence, Option C is the correct answer.

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A factory increased its production by 22.5 % and produced 49000tonnes. How many tonnes was it producing before?

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3 years ago

Price ($)87654321Price of CupsFind the unit rate ofthe price per cup.$[?]$54 cups 1 cup=Give your answer asa decimal.

Yanka [14]

Solution

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the formula for slope

$m=\frac{y_2-y_1}{x_2-x_1}$

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8 0

1 year ago

5 more than the quotient of a number and 8 is 42

Zepler [3.9K]

Answer:

The number is 296.

Step-by-step explanation:

Let's call "x" to the number we are looking for.

Now, the problem states that "5 more than the quotient of a number and 8 is 42". This means that this number is being divided by 8, it's also being additioned 5 and the final result is 42. Therefore, the expression of this operations on this number is the following:

$\frac{x}{8}+5=42$ . Let's solve the equation to find x.

1. Write the expression.

$\frac{x}{8}+5=42$

2. Substract 5 from both sides and simplify.

$\frac{x}{8}+5-5=42-5\\\\\frac{x}{8}=37\\\\$

3. Multiply 8 on both sides and simplify.

$8*\frac{x}{8}=37*8\\\\x=296$

We have found our number, it's 296!

3 0

2 years ago

Read 2 more answers

Find the midpoint of the segment with the given endpoints. (9,9) and (-1,- 3)

GenaCL600 [577]

Answer: (4, 3)

Step-by-step explanation:

The formula for coordinate of the mid point is given as :

Mid point = ( $\frac{x_{2}+x_{1}}{2}$ , $\frac{y_{2}+y_{1}}{2}$ )

$x_{1}$ = 9

$x_{2}$ = -1

$y_{1}$ = 9

$y_{2}$ = -3

Substituting the values into the formula , we have :

Mid-point = ( $\frac{-1+9}{2}$ , $\frac{-3+9}{2}$ )

Mid-point = ( $\frac{8}{2}$ , $\frac{6}{2}$ )

Mid - point = ( 4 , 3)

8 0

3 years ago

Im having a mental breakdown can someone please just do this for me

topjm [15]

The slopes of the original function y = |x| are m = 1 and m = -1 (m is the variable used to represent slope).

when you add a coefficient (number) in front of |x|, it will either make the slopes steeper or more flat. the larger the value of the coefficient, the steeper the slope will be (vice versa for a coefficient smaller than 1, which would make the slope more flat than the parent(original) function).

because these are absolute value functions, they will have two slopes. one slope for the end going up from left to right, and one for the end going down from left to right. this means that one slope must be positive and the other slope must be negative for each function.

with this in mind, the slopes of y = 2|x| are m = 2 and m = -2. the coefficient of 2 narrows the function by a factor of 2 (it is twice as narrow as the parent function). the same rules apply to y = 4|x| with the slopes of this function as m = -4 and m = 4 (it is 4 times narrower than the parent function).

with the fraction coefficients, the function is being widened. therefore, the slopes of y = 1/2 |x| are m = -1/2 and m = 1/2. the slopes of y = 1/5 |x| are m = -1/5 and m = 1/5.

6 0

2 years ago