3x + y = 0 and x-y =4 intercept graph
To graph the equations 3x + y = 0 and x - y = 4 and find their intercepts, you can use multiple methods. Here's how you can approach it:
1. Intercepts of 3x + y = 0:
To find the x-intercept, set y = 0 in the equation:
3x + 0 = 0
Solve for x: x = 0
Therefore, the x-intercept is (0, 0).
To find the y-intercept, set x = 0 in the equation:
3(0) + y = 0
Solve for y: y = 0
Therefore, the y-intercept is (0, 0).
2. Intercepts of x - y = 4:
To find the x-intercept, set y = 0 in the equation:
x - 0 = 4
Solve for x: x = 4
Therefore, the x-intercept is (4, 0).
To find the y-intercept, set x = 0 in the equation:
0 - y = 4
Solve for y: y = -4
Therefore, the y-intercept is (0, -4).
Now, let's plot these points on a graph:
- We have the intercept (0, 0) for both equations.
- For 3x + y = 0, add another point (4, -12) by substituting x = 4 into the equation to get the y-coordinate. (3 * 4) + y = 0 -> 12 + y = 0 -> y = -12.
- For x - y = 4, add another point (0, -4) by substituting y = -4 into the equation to get the x-coordinate. x - (-4) = 4 -> x + 4 = 4 -> x = 0.
Plotting these points will give you two intersecting lines on the graph.