How to graph the following equation and identify y-intercept 2y+3x= -2?

London Lawson

London Lawson

Answered question

2023-01-31

How to graph the following equation and identify y-intercept 2 y + 3 x = - 2 ?

Answer & Explanation

Keegan Herman

Keegan Herman

Beginner2023-02-01Added 6 answers

1) Put the equation into Slope-Intercept form ( y = m x + b ).
2 y + 3 x = - 2
2 y + 3 x - 3 x = - 2 - 3 x
2 y = - 2 - 3 x
- 1 ( 2 y = - 2 - 3 x )

Note: I multiplied the equation by - 1 to show how you make this equation would resemble the formula. You don't have to do this step for this particular equation though because the answers are negative anyway.

- 2 y = 2 + 3 x

Note: Because of the Commutative Property of Addition you can rearrange the equation to look like the formula

- 2 y = 3 x + 2
- 2 y = 3 x + 2 - 2
y = - 3 2 x + ( - 2 2 )
Now that the equation is in Slope Intercept form ( y = m x + b ) you know the slope ( m ) and the y-intercept ( b ).
2) Find the *x-intercept*
To find the x-intercept you need to set y equal to 0

Note: You could use the new equation as well, but I'll use the original equation because it is quicker.

2 y + 3 x = - 2
2 ( 0 ) + 3 x = - 2
3 x = - 2
3 x = - 2 3
x = - 2 3
Now that you are aware of these facts:

The slope is - 3 2 , this means the graph will be going down or decreasing
The y-intercept is - 1 , this means the graph crosses the y-axis at the point ( 0 , - 1 )
The x-intercept is - 2 3 , this means the graph crosses the x-axis at the point ( - 2 3 , 0 )

You can either:
Plot the coordinates of the x and y-intercepts and use the slope to create a line
OR
Use the Slope Intercept form equation to create points ranging between the two intercepts and then connect the dots

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