given 3y +2x=-6
2.5.1 calculate the x-intercept and y-intercept
2.5.2 sketch the graph 3y + 2x =-6 on a cartesian plane
To find the x-intercept and y-intercept, we need to substitute 0 for y and solve for x to find the x-intercept, and substitute 0 for x and solve for y to find the y-intercept.
1. To find the x-intercept:
Substitute y = 0 in the equation:
3(0) + 2x = -6
0 + 2x = -6
2x = -6
x = -6/2
x = -3
So, the x-intercept is (-3, 0).
2. To find the y-intercept:
Substitute x = 0 in the equation:
3y + 2(0) = -6
3y + 0 = -6
3y = -6
y = -6/3
y = -2
So, the y-intercept is (0, -2).
To sketch the graph of 3y + 2x = -6 on a Cartesian plane, we can use the intercepts we just found (-3, 0) and (0, -2). Let's plot these points and draw a line passing through them.
The x-intercept is -3, so we go 3 units to the left on the x-axis and mark a point.
The y-intercept is -2, so we go 2 units down on the y-axis and mark a point.
Now, draw a line passing through these two points.
The graph of 3y + 2x = -6 is a straight line passing through the points (-3, 0) and (0, -2).
I apologize, as an AI text-based model, I am unable to provide a visual representation of the graph. I hope the instructions provided help you sketch the graph accurately.
To find the x-intercept and y-intercept of the equation 3y + 2x = -6, you need to set either x or y to zero and solve for the other variable.
2.5.1 Calculating the x-intercept:
To find the x-intercept, set y = 0 and solve for x.
Replace y with 0 in the equation:
3(0) + 2x = -6
0 + 2x = -6
2x = -6
Divide both sides of the equation by 2:
x = -6/2
x = -3
So the x-intercept is -3.
2.5.1 Calculating the y-intercept:
To find the y-intercept, set x = 0 and solve for y.
Replace x with 0 in the equation:
3y + 2(0) = -6
3y + 0 = -6
3y = -6
Divide both sides of the equation by 3:
y = -6/3
y = -2
So the y-intercept is -2.
2.5.2 Sketching the graph on a Cartesian plane:
To sketch the graph of the equation 3y + 2x = -6 on a Cartesian plane, you can use the intercepts we just calculated.
Plot the x-intercept (-3) on the x-axis where y = 0. This will be a point on the line.
Plot the y-intercept (-2) on the y-axis where x = 0. This will be another point on the line.
Now, draw a straight line connecting these two points. This line represents the graph of the equation 3y + 2x = -6 on the Cartesian plane.
To find the x-intercept, we set y equal to 0 and solve for x. Similarly, to find the y-intercept, we set x equal to 0 and solve for y.
2.5.1 Calculate the x-intercept:
Let y = 0 in the equation 3y + 2x = -6:
3(0) + 2x = -6
0 + 2x = -6
2x = -6
x = -6/2
x = -3
So, the x-intercept is -3.
2.5.1 Calculate the y-intercept:
Let x = 0 in the equation 3y + 2x = -6:
3y + 2(0) = -6
3y + 0 = -6
3y = -6
y = -6/3
y = -2
Therefore, the y-intercept is -2.
2.5.2 Sketch the graph of 3y + 2x = -6 on a Cartesian plane:
To sketch the graph, start by plotting the x-intercept (-3) and the y-intercept (-2).
Plot the point (-3, 0) and (0, -2) on the Cartesian plane.
Then, draw a straight line passing through these two points. This line represents the graph of the equation 3y + 2x = -6.
Please note that without the specific values for the x and y-axis limits, it is not possible to accurately sketch the graph.