Question

Rewrite the following equation in slope-intercept form.

10x − 10y = –1 ?


Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answer 1

y = x + 1/10

Explanation:

Rewrite the following equation in slope-intercept form: 10x − 10y = –1 ?

slope intercept form: y = mx + b so you are solving for y:

10x − 10y = –1

subtract 10x from both sides:

10x − 10y – 10x = –1 – 10x

-10y = –1 – 10x

divide all terms by -10:

-10y/(-10) = –1/(-10) – 10x/(-10)

y = 1/10 + x

rearrange for slope intercept form: y = mx + b

y = x + 1/10

Answer 2

`y=x+(1)/(10)`

Explanation:

`\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}`

Given equation:

`10x-10y=-1`

To write the given equation in slope-intercept form, perform algebraic operations to isolate y.

Add 10y to both sides of the equation:

`\implies 10x-10y+10y=10y-1`

`\implies 10x=10y-1`

Add 1 to both sides of the equation:

`\implies 10x+1=10y-1+1`

`\implies 10x+1=10y`

`\implies 10y=10x+1`

Divide both sides of the equation by 10:

`\implies (10y)/(10)=(10x+1)/(10)`

`\implies (10y)/(10)=(10x)/(10)+(1)/(10)`

`\implies y=x+(1)/(10)`

Therefore, the given equation in slope-intercept form is:

`\boxed{y=x+(1)/(10)}`