A coordinate plane shows four quadrants with both the x-axis and the y-axis ranging from negative 10 to positive 10 in increments of 2. Two points are plotted and joined by a line. The plotted points are as follows: left parenthesis negative 8 comma 0 right parenthesis, left parenthesis 0 comma 4 right parenthesis. A line connects the two plotted points and extends beyond the points in both directions.
To plot the points and draw the line on the coordinate plane, we start by drawing the x-axis and the y-axis ranging from -10 to 10 in increments of 2.
The x-axis will have the values -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10.
The y-axis will have the values -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10.
Next, we plot the points (-8, 0) and (0, 4) on the coordinate plane. The point (-8, 0) is to the left of the y-axis, on the x-axis, and the point (0, 4) is above the x-axis, on the y-axis.
Finally, we draw a line connecting the two plotted points (-8, 0) and (0, 4). This line extends beyond the plotted points in both directions.
The final coordinate plane should look like this:
| 10
|
|
|
| -8
---------------------------------------
|-10 -6 -2 2 6 10
|
|
|
|
-10
To describe the line connecting the plotted points (-8, 0) and (0, 4), let's find the slope and y-intercept of the line using the formula:
Slope (m) = (change in y) / (change in x)
Using the coordinates (-8, 0) and (0, 4), the change in y = 4 - 0 = 4, and the change in x = 0 - (-8) = 8.
So, the slope (m) = 4/8 = 1/2.
To find the y-intercept, we can choose any of the given points (x, y) to substitute into the line equation:
y = mx + b
Using the point (0, 4) and slope (m = 1/2), we can solve for the y-intercept (b):
4 = (1/2)(0) + b
4 = 0 + b
b = 4
So, the equation of the line connecting the points (-8, 0) and (0, 4) is:
y = (1/2)x + 4
Now we can plot this line on the coordinate plane.
To understand the given information, let's break it down step by step.
1. The coordinate plane: A coordinate plane is a two-dimensional plane formed by two perpendicular lines called the x-axis and the y-axis. The x-axis ranges from negative 10 to positive 10 in increments of 2, while the y-axis also ranges from negative 10 to positive 10 in increments of 2. This means there are four quadrants on the coordinate plane.
2. Plotted points: Two points have been plotted on the coordinate plane. The first point is (-8, 0), which means it is located 8 units to the left of the y-axis and on the same level as the x-axis. The second point is (0, 4), which means it is located on the x-axis, 4 units above the origin (where the x-axis and y-axis intersect).
3. Connecting the points: These two plotted points are joined by a line. The line passes through both points and extends beyond them in both directions. This line represents all the infinite points that lie along it.
In summary, the given information describes a coordinate plane with four quadrants, two points plotted at (-8, 0) and (0, 4), and a line that connects these two points and extends indefinitely in both directions.