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

Question

Hazel Anglin · Accepted Answer

graph{(-3/2)x-1 [-1.32, 1.198, -1.118, 0.14]}
The y-intercept is #-1# 1) Put the equation into Slope-Intercept form (#y=mx+b#). #2y+3x=-2# #2y+cancel(3x color(red)(-3x))=-2-color(red)(3x)# #2y=-2-3x# #color(blue)(-1)*(2y=-2-3x)# #-2y=2+3x# #-2y=3x+2# #(-2y=3x+2)/-2# #y=-3/2x+color(green)[(-2/2)# Now that the equation is in Slope Intercept form (#y=mx+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# #2color(orange)y+3x=-2# #2color(orange)[(0)]+3x=-2# #3x=-2# #(3x=-2)/3# #x=-2/3# Now, that you know the following: 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

Savannah Anderson · Answer

undefined To graph the equation $2y + 3x = -2$, first solve for $y$ to put the equation in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Solve for $y$:
$$2y = -3x - 2$$
$$y = -\frac{3}{2}x - 1$$

The slope ($m$) is $-\frac{3}{2}$ and the y-intercept ($b$) is $-1$.

To graph the equation, plot the y-intercept at $y = -1$ on the y-axis, then use the slope to find another point, and draw a line through those two points.