Given 3x-2y=6, how do i find the area of triangle OPQ? I know I have to graph the equation first but I don't even know how to find the points?
To graph an equation, pick a value for one variable (x) and calculate the value of y for that value of x. This gives you the coordinates for one point.
Do the same for other values of x. After you have an adequate number of coordinates, play "connect the dots."
I hope this helps. Thanks for asking.
I assume - although you haven't said so - that P and Q are the points at which the line you've given cuts the X and Y axes respectively. If so, then P is the point (2,0) and Q is (0,-3). (To get those, just put Y=0 and solve your equation for X, then put X=0 and solve it for Y.) You've now got the three vertices of your triangle, and you want to calculate the area of it. But this is a right-angled triangle (look at the graph), and you already know the width and the height of it. So the area is just half the width times the hight.
To find the points for triangle OPQ, we need to solve the given equation for two different values of x and y. Let's start by graphing the equation on a coordinate plane:
1. Convert the given equation into the slope-intercept form (y = mx + b).
3x - 2y = 6
-2y = -3x + 6
y = 3/2x - 3
2. Plot the y-intercept point (0, -3). This point is found by substituting x = 0 into the equation and solving for y.
3. Identify the slope (m) of the equation, which is 3/2. This tells us how much we move vertically and horizontally from the y-intercept.
The slope tells us that for every 2 units moved horizontally (right or left), we move 3 units vertically (up or down).
4. Using the slope, we can find additional points on the line by counting from the y-intercept. For example, if you move 2 units to the right, you move 3 units up to (2, 0). Similarly, if you move 2 units to the left, you move 3 units down to (-2, -6). Plot these points on the graph.
5. Connect the points on the graph to form a straight line. This line represents the given equation, and any point on the line satisfies the equation.
Now, to find the points for triangle OPQ, you will need additional information. The equation 3x - 2y = 6 represents a line, but we need more details about the triangle's vertices or any angles involved to determine the exact points O, P, and Q.
Please provide additional information about the triangle, such as the coordinates of any of its vertices or any angles specified, so that we can assist you further in finding the area of triangle OPQ.