graph linear equation 3x-6y-9=0
I am not sure what grade you are.
To graph the equation manually the usual way is to rearrange it in the form y=??
then calculate y for a range of values of x. Then plot y values against the x values. In fact you only need to do this for two values of x and draw a line beteeen them as it is a straight line equation.
Higher grade students will recognise the similarity of the equation with y=mx+c.
That can also be written in standard form as
y = x/2 - (3/2)
The slope of the line is 1/2 and it passes through the point (x = 0, y = -3/2)
You will have to draw the graph yourself. It isn't hard.
To graph the linear equation 3x - 6y - 9 = 0, we can follow these steps:
Step 1: Rewrite the equation in the slope-intercept form (y = mx + b), where "m" is the slope and "b" is the y-intercept.
Let's rearrange the given equation:
3x - 6y - 9 = 0
-6y = -3x + 9
Divide both sides by -6:
y = 1/2x - 3/2
Step 2: Identify the slope and y-intercept.
The equation is now in the form y = mx + b, where the slope "m" is 1/2 and the y-intercept "b" is -3/2.
Step 3: Start by plotting the y-intercept.
The y-intercept is -3/2, which means the line intersects the y-axis at the point (0, -3/2). Mark this point on the coordinate plane.
Step 4: Use the slope to find other points.
The slope of 1/2 means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 1/2. Similarly, for every decrease of 1 in the x-coordinate, the y-coordinate decreases by 1/2.
Starting from the y-intercept (0, -3/2), we can move 1 point to the right (increasing x by 1) and 1/2 point up (increasing y by 1/2) to get the next point. Plot this point.
Similarly, from the y-intercept, we can move 1 point to the left (decreasing x by 1) and 1/2 point down (decreasing y by 1/2) to get another point. Plot this point.
Step 5: Connect the points.
Once you have at least two points, you can extend the line through them. Use a straight edge or ruler to draw a line that passes through both points, extending infinitely in both directions. This line represents the graph of the equation.
That's it! You have successfully graphed the linear equation 3x - 6y - 9 = 0.