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3 years ago

Identify an equation in slope-intercept form for the line parallel to y = 5x + 2

Mathematics

1 answer:

Elanso [62]3 years ago

6 0

Answer:

D. y = 5x + 29

Step-by-step explanation:

To write an equation of a line in slope-intercept form, we need to find the slope and the y-intercept.

The equation of a line is y=mx + b.

x and y are the coordinates of any point on a line.

m is the slope.

b is the y-intercept.

Lines are parallel to each other when they have the same slope. A line parallel to y = 5x + 2 would also have the slope 5.

m = 5

Since we have a point on the line, (-6, -1) and the slope, 5, there is only one missing variable, b, the y-intercept.

Substitute the known information into the equation and isolate b.

y = mx + b

-1 = 5(-6) + b <=Simplify by solving 5 X -6

-1 = -30 + b

-1 + 30 = -30 + 30 + b <= Add 30 to both sides to isolate b

29 = b

b = 29 <= Standard formatting puts the variable on the left side

Put the m and b values into the equation of a line to solve:

y = mx + b

y = 5x + 29

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Let a = x^2 + 4. Rewrite the following equation in terms of a and set it equal to zero. ( x^2 + 4 )^2 +32 = 12x^2 + 48

Aleks04 [339]

Answer: In the resulting equation: " a² - 12a + 32 = 0 " ;
________________________________________________________
The "coefficient" of the "a" term is: " - 12" .
________________________________________________________
The "constant" is: " 32 " .
________________________________________________________

Explanation:
________________________________________________________

Let: "a = x² + 4 " .

Given: (x² + 4)² + 32 = 12x² + 48 ;
______________________________________________________

Factor: "12x² + 48" into " (x² + 4) " ;

"12x² + 48" = 12 (x² + 4) " ;
______________________________________________________

Given: (x² + 4)² + 32 = 12x² + 48 ;

rewrite as; "a² + 32 = 12a " ;

Subtract "12a" from each side of the equation;

"a² + 32 - 12a = 12a - 12a ;

to get:

" a² - 12a + 32 = 0 " .
___________________________________________________
The coefficient of the "a" term; that is:

The "coefficient" of " -12a" ; is: "- 12" .

The constant is: "32<span>" .
</span>___________________________________________________

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3 years ago

What is the rational expression in simplest form? State any restrictions on the variables.

allochka39001 [22]

According to the question, the given rational expression can be simplified which is as shown below:

Rational expression = $\frac{12-4x}{x^{2} -9}=\frac{4(3-x)}{(x-3)(x+3)}$

For the simplification of the given expression, calculate the factors of the numerator as well as denominator terms and divide them from each other. In this change the sign of the expression before dividing with each other.

Rational expression = $\frac{-4}{(x+3)}$

The rational expression are also known as polynomial expression. The highest degree of these expression is two. And these expression uses concept of factor rule.

Therefore, the final expression is $\frac{-4}{(x+3)}$

What is polynomial expression?

Polynomial expression are those equation whose highest degree is two. It is also called as quadratic equation. And it is simplified by performing the factors on the given expressions.

To learn more about the polynomial expression from the given link:

<u>brainly.com/question/1280754</u>

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mote1985 [20]

<h2>Answer:</h2>

For a real number a, a + 0 = a. TRUE

For a real number a, a + (-a) = 1. FALSE

For a real numbers a and b, | a - b | = | b - a |. TRUE

For real numbers a, b, and c, a + (b ∙ c) = (a + b)(a + c). FALSE

For rational numbers a and b when b ≠ 0, is always a rational number. TRUE

<h2>Explanation:</h2>

<u>For a real number a, a + 0 = a. </u><u>TRUE</u>

This comes from the identity property for addition that tells us that<em> zero added to any number is the number itself. </em>So the number in this case is $a$ , so it is true that: