The equation you provided is 3x - 4y = -8. This is a linear equation in standard form.
To work with this equation, let's rearrange it into slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
To convert the equation to slope-intercept form, we isolate y:
3x - 4y = -8
-4y = -3x - 8
y = (3/4)x + 2
Now, we can see that the slope (m) of the line is 3/4, and the y-intercept (b) is 2.
To plot this line on a graph, we can start by plotting the y-intercept, which is the point (0, 2). From there, we can use the slope to find additional points on the line.
Using the slope of 3/4, we can determine that for every 4 units we move to the right along the x-axis, we move up 3 units along the y-axis. Similarly, for every 4 units we move to the left along the x-axis, we move down 3 units along the y-axis.
By plotting a few more points, we can sketch the line:
Point 1: (0, 2) - the y-intercept
Point 2: (4, 5) - move to the right 4 units and up 3 units
Point 3: (-4, -1) - move to the left 4 units and down 3 units
Connecting these points, we can draw a straight line that represents the equation 3x - 4y = -8.
I hope this helps!