# How do you graph using slope and intercept of 3x-y=2?

Jul 12, 2018

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#### Explanation:

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We are given the liner equation: color(red)(3x-y=2

The standard form of a linear equation in the slope-intercept form is:

color(blue)(y = f(x) = mx+b, where

color(blue)(m is the slope and

color(blue)(b is the y-intercept.

We rewrite the linear equation color(red)(3x-y=2 in the slope-intercept form:

color(red)(3x-y=2

Subtract $\textcolor{red}{3 x}$ from both sides of the equation.

3x-y-color(red)(3x)=2-color(red)(3x

cancel(3x)-y-color(red)(cancel(3x)=2-color(red)(3x

$- y = 2 - 3 x$

Multiply both sides of the equation by color(red)((-1)

$\left(- 1\right) \left(- y\right) = \left(- 1\right) \left(2 - 3 x\right)$

color(green)(y = 3x-2

We now have our linear equation in the slope-intercept form:

Slope =color(blue)(3/1 and y-intercept =color(blue)((-2)

color(green)(Slope = (Run)/(Rise)

Slope can also be defined as (Change in y)/(change in x)

On a graph, plot the point on the y-axis, at the point color(blue)((-2)

From this point color(blue)((y=-2), move up $2$ points and move right by $1$ point. Plot a point there.

Join these two points to get the required graph:

Hope it helps.