Question

Helppp me i need help plzzzzz

Answer 1

Problem:

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?

Choices:

○ 10x + 3y - 1 = 0

○ x + 3y + 10 = 0

○ x + 3y - 10 = 0

Remember to use this formula:

`\quad \quad\quad\quad\boxed{\tt{y = mx + b}}`

Given that:

`\quad \quad\quad\quad\boxed{\tt{Slope (m) = (1)/(3) }}`

`\quad \quad\quad\quad\boxed{\tt{y \: intercept(b) = (10)/(3) }}`

Lets try!

`\quad \quad\quad\quad\boxed{\tt{y = - ( 1)/(3)x + (10)/(3) }}`

Then convert it in general form using this formula:

`\quad \quad\quad\quad\boxed{\tt{ax + by + c = 0}}`

Each side will be multiply by 3

`\quad \quad\quad\quad\boxed{\tt{ (3)y = 3(- ( 1)/(3)x + (10)/(3) )}}`

`\quad \quad\quad\quad\boxed{\tt{ 3y = \cancel{ \color{red}3}(- \frac{ 1}{ \cancel{ \color{red}3}}x + \frac{10}{ \cancel{ \color{red}3}} )}}`

`\quad \quad\quad\quad\boxed{\tt{3y = - x + 10}}`

Let's convert "x" like this.

`\quad\quad\quad\boxed{\tt{3y = - x + 10}} \: ➡ \: \boxed{\tt{x + 3y = 10}}`

Convert "10" like this.

`\quad\quad\quad \boxed{\tt{x + 3y = 10}} \: ➡ \: \boxed{ \tt{x + 3y - 10 = 0}}`

Hence, the answer is:

`\quad \quad\quad\quad \boxed{ \color{green}{ \tt{x + 3y - 10 = 0}}}`

_________

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Answer 2

x+3y -10 =0

Explanation:

In slope intercept form

y = mx+b where m is the slope and b is the y intercept

y = -1/3x +10/3

We want it in the general form ax+by +c =0 where a,b,c are integers and a>0

Multiply by 3 on each side

3*y = 3(-1/3x +10/3)

3y = -x +10

Add x to each side

x+3y = -x+10 +x

x+3y = 10

Subtract 10 from each side

x+3y -10 = 10-10

x+3y -10 =0