Question

How do you write `y=-3/4x+5/2` in standard form?

Answer 1

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Linear Equation in Standard Form : `color(blue)(3x+4y=10`

Explanation:

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You are given a Linear Equation : `color(red)(y=-3/4x+5/2`

The Standard Form for a linear equation in two variables, `x` and `y`, is

`color(green)(Ax+By=C`, where

`color(green)(A, B and C` are all integer values.

Consider the given Linear Equation : `color(red)(y=-3/4x+5/2`

Multiply both sides of the equation by 4

`=>4*y=4[-3/4x+5/2]`

`rArr 4y=-4(3/4)x+4(5/2)`

`rArr 4y=-cancel 4(3/cancel 4)x+cancel 4^color(red)(2)(5/cancel 2)`

`rArr 4y=-3x+(2)(5)`

`rArr 4y=-3x+10`

Move the term `3x` to the left hand side of the equation by adding `3x` to both sides.

`rArr 4y+3x=-3x+10+3x`

`rArr 4y+3x=-cancel (3x)+10+cancel(3x)`

Rearrange the terms on the left hand side to bring the equation to the Standard Form.

`3x+4y=10`

Hence, `color(blue)(4x+3y=10` is the required equation in Standard Form.

Hope you find the solution process helpful.