Question

-3x+4y=8
Convert the equation from standard form to slope intercept form

Answer 1

y = (3/4)x + 2

Explanation:

Now we have to write,

→ The equation in slope-intercept form.

The equation is,

→ -3x + 4y = 8

The slope-intercept form is,

→ y = mx + b

Let's rewrite the given equation,

→ -3x + 4y = 8

→ 4y = 8 + 3x

→ 4y = 3x + 8

→ y = (3x + 8)/4

→ y = (3x/4) + (8/4)

→ [ y = (3/4)x + 2 ]

Hence, the answer is y = (3/4)x + 2.

Answer 2

`\large\boxed{ \tt y=(3)/(4)x+2}`

Explanation:

`\textsf{We are asked to convert the given equation from standard form to slope-intercept form.}`

`\textsf{Standard form is a more complex form of a linear equation.}`

`\textsf{Let's review important information necessary.}`

`\large\underline{\textsf{Standard Form;}}`

`\tt Ax+By=C`

`\textsf{For this equation, A, B, and C are integers.}`

`\textsf{C is the y-intercept.}`

`\textsf{A is the slope.}`

`\textsf{B represents how many times the whole equation \underline{was} multiplied by.}`

`\underline{\textsf{A more simplified equation;}}`

`\tt x + y = c`

`\textsf{We need to change this equation into slope-intercept form.}`

`\large\underline{\textsf{Slope-Intercept Form;}}`

`\tt y = mx+b`

`\textsf{Note that this equation \underline{isn't} multiplied.}`

`\textsf{M represents the slope.}`

`\textsf{B represents the y-intercept.}`

`\textsf{We should change where the y is, and divide the equation by how much B is.}`

`\large\underline{\textsf{To Start;}}`

`\tt-3x+4y=8`

`\textsf{The y-intercept is 8.}`

`\textsf{The slope is -3.}`

`\textsf{The equation is multiplied by 4, so we should divide by 4.}`

`\large\underline{\textsf{Divide by 4;}}`

`\tt (-3x+4y)/(4) =(8)/(4)`

`\tt -(3)/(4)x+y=2`

`\textsf{Now, for slope-intercept form, y has to \underline{equal} the slope and the y-intercept added together.}`

`\textsf{Modify the equation where y is the result by adding the slope to both sides.}`

`\large\underline{\textsf{Change into Slope-Intercept Form;}}`

`\tt -(3)/(4)x+y=2`

`\tt -(3)/(4)x + (3)/(4)x+y=2 + (3)/(4) x`

`\underline{\textsf{Switch around the slope and the y-intercept;}}`

`\large\boxed{ \tt y=(3)/(4)x+2}`