Without building the graph, find the coordinates of the points of intersection of the graph of the equation (x+2)(y+3)=0 with the x- and y-axes
Oh, finding the points of intersection without building the graph? That's like trying to eat pizza without using your hands – it's possible, but also a little messy!
Alright, let's solve this equation step by step to find the points of intersection.
To begin, let's consider the x-axis. When a point lies on the x-axis, its y-coordinate is always zero. So we can set y+3 equal to zero and solve for x:
y + 3 = 0
y = -3
So our first point of intersection on the x-axis is (-2, 0), where x is -2 and y is 0.
Next, let's consider the y-axis. When a point lies on the y-axis, its x-coordinate is always zero. So we can set x+2 equal to zero and solve for y:
x + 2 = 0
x = -2
Hence, our second point of intersection on the y-axis is (0, -3), where x is 0 and y is -3.
Voila! We've found the coordinates of the points of intersection of the equation (x+2)(y+3)=0 with the x- and y-axes. Now you can build the graph or enjoy a slice of humor-infused pizza!
To find the coordinates of the points of intersection of the graph of the equation (x+2)(y+3)=0 with the x-axis and y-axis, we can set each axis value to zero separately.
1. Points of intersection with the x-axis:
To find the x-intercepts, we set y equal to zero:
x + 2 = 0
x = -2
So the point of intersection with the x-axis is (-2, 0).
2. Points of intersection with the y-axis:
To find the y-intercepts, we set x equal to zero:
0 + 2(y + 3) = 0
y + 3 = 0
y = -3
So the point of intersection with the y-axis is (0, -3).
Therefore, the coordinates of the points of intersection with the x-axis and y-axis are (-2, 0) and (0, -3) respectively.
To find the coordinates of the points of intersection of the graph with the x-axis, we need to consider the equation (x + 2)(y + 3) = 0.
For a point to lie on the x-axis, the y-coordinate must be 0. Therefore, we substitute y = 0 into the equation:
(x + 2)(0 + 3) = 0
(x + 2)(3) = 0
From this equation, we can see that the only way for the product to be zero is if (x + 2) = 0. Solving for x, we get:
x + 2 = 0
x = -2
So, one point of intersection with the x-axis is (-2, 0).
Now, to find the coordinates of the points of intersection with the y-axis, we need to consider the equation (x + 2)(y + 3) = 0.
For a point to lie on the y-axis, the x-coordinate must be 0. Therefore, we substitute x = 0 into the equation:
(0 + 2)(y + 3) = 0
(2)(y + 3) = 0
From this equation, we can see that the only way for the product to be zero is if (y + 3) = 0. Solving for y, we get:
y + 3 = 0
y = -3
So, one point of intersection with the y-axis is (0, -3).
In summary, the coordinates of the points of intersection of the graph of the equation (x + 2)(y + 3) = 0 with the x-axis are (-2, 0), and with the y-axis are (0, -3).
set x=0 to find y
set y=0 to find x