Solve for x . Enter the solutions from least to greatest.

The slope of a line is -1/3, and the y-intercept is 10/3. What is the equation of the line written in general form?

Y_Kistochka [10]

The answer is: [B]: " x + 3y + 10 = 0 " .
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Explanation:
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Note the equation for a line; in 'slope-intercept form': "y = mx + b" ;

in which "y" is isolated alone, as a single variable, on the left-hand side of the equation;
"m" = the slope of the line; and is the co-efficient of "x" ;
b = the "y-intercept"; (or the "y-coordinate of the point of the "y-intercept").
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So, given the information in this very question/problem:
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slope = m = (-1/3) ;
b = y-intercept = (10/3) ;
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And we can write the equation of the line; in "slope-intercept form"; that is:
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" y = mx + b " ; as:
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" y = (-1/3)x + (10/3) " ;
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Now, the problem asks for the equation of this line; in "general form"; or "standard format"; which is:
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"Ax + By + C = 0 " ;
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So; given:
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" y = (-1/3)x + (10/3) " ;
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We can multiply the ENTIRE EQUATION (both sides) by "3" ; to get rid of the "fractions" ;

→ 3* { y = (-1/3)x + (10/3) } ;

→ 3y = -1x + 10 ;

↔ -1x + 10 = 3y ;

Subtract "(3y)" from each side of the equation:
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-1x + 10 − 3y = 3y − 3y ;

to get:

-1x + 10 − 3y = 0 ;

↔ -1x − 3y − 10 = 0 ;

→ This is not one of the "3 (THREE) answer choices given" ;

→ So, multiply the ENTIRE EQUATION (both sides); by "-1" ; as follows:

-1 * {-1x − 3y − 10 = 0} ;

to get:
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→ " x + 3y + 10 = 0 " ; which is: "Answer choice: [B] ."
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Note that is equation is in the "standard format" ;
→ " Ax + By + C = 0 " .
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6 0

3 years ago

Read 2 more answers

Liam spent $4.76 on a salad bowl, and $3.81 on a cup of coffee. He paid using TWO ten dollar bills. What was Liam's change?

quester [9]

Answer:

11.43

Step-by-step explanation:

You can start this by adding the total cost of the salad and the coffee.

4.76 + 3.81 = 8.57

Then you have the paid amount of 20 bucks because there was two tens.

20 - 8.57 = 11.43.

3 0

3 years ago

Read 2 more answers

I'm doing an online course to study for a test. Can someone please explain how to do this? :(

Leona [35]

Hi there

This is how you read the question: What is the cube root of 64.
To answer this question ask yourself what number multiplied by itself three times gives you the answer 64?
1*1*1=1
2*2*2=8
3*3*3=27
4*4*4=64
YAY! that means the answer is 4.

Hope this helps.
And you give me the brainliest answer.
Thanks

8 0

3 years ago

Read 2 more answers

WILL MARK BRAINLIEST

Nataliya [291]

I believe the second one : drawing a number from a hat, not replacing it, and then drawing a second number

5 0

2 years ago

Read 2 more answers

Use long or synthetic division to find the following quotients (x^3+2x^2!22x-45)÷(x+5)

svetoff [14.1K]

Answer:

$\boxed{\textsf{ The quotient is $\sf x^2-3x-7$ and the remainder is (-10).}}$

Step-by-step explanation:

Here we will be using long division method to find the quotient . Here we need to divide (x³+2x²-22x-45) and (x+5) . So lets divide .

x+5) x³+2x²-22x-45 ( x² -3x -7

x³ + 5x²

- -

______________

- 3x²-22x -45

-3x² -15x

+ +

______________

-7x -45

-7x -35

______________

-10

Quotient = x² -3x -7

Remainder = (-10)

<h3>★Hence the quotient is x² -3x -7 and the remainder is (-10) .</h3>

7 0

3 years ago