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

Jun 9, 2018

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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

$\implies 4 \cdot y = 4 \left[- \frac{3}{4} x + \frac{5}{2}\right]$

$\Rightarrow 4 y = - 4 \left(\frac{3}{4}\right) x + 4 \left(\frac{5}{2}\right)$

$\Rightarrow 4 y = - \cancel{4} \left(\frac{3}{\cancel{4}}\right) x + {\cancel{4}}^{\textcolor{red}{2}} \left(\frac{5}{\cancel{2}}\right)$

$\Rightarrow 4 y = - 3 x + \left(2\right) \left(5\right)$

$\Rightarrow 4 y = - 3 x + 10$

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

$\Rightarrow 4 y + 3 x = - 3 x + 10 + 3 x$

$\Rightarrow 4 y + 3 x = - \cancel{3 x} + 10 + \cancel{3 x}$

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

$3 x + 4 y = 10$

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

Hope you find the solution process helpful.