Here we will show you how to calculate and provide solutions to math problems related to 2x + 3y = 6.
We will start by calculating and showing you the solution for the x-intercept and y-intercept of 2x + 3y = 6.
Then, we will show you how to get the graph plot coordinates for 2x + 3y = 6 so we can illustrate it on a graph.
Finally, we will solve 2x + 3y = 6 for x and also for y, then calculate and show you the solution for the slope of 2x + 3y = 6.
Find x-intercept
The x-intercept is where the graph crosses the x-axis. To find the x-intercept, we set y1=0 and then solve for x.
2x + 3y = 6
2x + 3(0) = 6
x1 = 3 y1 = 0
Find y-intercept
The y-intercept is where the graph crosses the y-axis. To find the y-intercept, we set x2=0 and then solve for y.
2x + 3y = 6
2(0) + 3y = 6
y2 = 2 x2 = 0
Get Graph Plot Coordinates
Getting two graph points will allow you to make a straight line on a graph. The plot coordinate format is (x1,y1) and (x2,y2).
Thus, we use the x-intercept and y-intercept results above to get the graph plots for 2x + 3y = 6 as follows:
(x1,y1) and (x2,y2)
(3,0) and (0,2)
Solve for x
To solve for x, we solve the equation so the variable x is by itself on the left side:
2x + 3y = 6
x = 3 - 1.5y
Solve for y
To solve for y, we solve the equation so the variable y is by itself on the left side:
2x + 3y = 6
y = 2 - 0.667x
Find slope
The slope of the line (m) is the steepness of the line. It is the change in the y coordinate divided by the corresponding change in the x coordinate. Simply plug in the coordinates from above and solve for m to get the slope for 2x + 3y = 6
m = (y2 - y1)/(x2 - x1)
m = (2 - 0)/(0 - 3)
m = -0.667
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