Question

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

Answer 1

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Please read the explanation.

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

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

`(-1)(-y)=(-1)(2-3x)`

`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.