Use the graph of y = x to determine an additional ordered pair (x, y) that satisfies the equation. Find the ordered pair (x, y) if the x-coordinate is 3.
(3, ____)
The coordinates are (0, 0), (1, 1), (2, 2)
(3, 3)
In a cleaning mixture, the amount of water is directly proportional to the amount of ammonia. A mix with 5 gallons of water requires 10 teaspoons of ammonia. How many gallons of water are needed for 25 teaspoons of ammonia? Write your answer in decimal form.
Since the amount of water is directly proportional to the amount of ammonia, we can set up a proportion to solve for the unknown amount of water.
Let x be the unknown amount of water in gallons, and 5 gallons of water correspond to 10 teaspoons of ammonia. Therefore, the proportion is:
5 gallons / 10 teaspoons = x gallons / 25 teaspoons
Solving this proportion:
5/10 = x/25
0.5 = x/25
x = 0.5 * 25
x = 12.5
25 teaspoons of ammonia would require 12.5 gallons of water.
Use the table to answer the question.
x, y | (x, y)
0 | (0, )
4 | (4, )
8 | (8, )
Complete the ordered pairs in the table by finding the y-coordinate of the ordered pairs for the equation y = 1/4x.
x, y | (x, y)
0 | (0, ____)
4 | (4, ____)
8 | (8, ____)
To find the missing y-coordinates for the ordered pairs in the table using the equation y = 1/4x, we substitute the given x-values into the equation:
1. For x = 0:
y = 1/4(0)
y = 0
Therefore, the ordered pair for x = 0 is (0, 0).
2. For x = 4:
y = 1/4(4)
y = 1
Therefore, the ordered pair for x = 4 is (4, 1).
3. For x = 8:
y = 1/4(8)
y = 2
Therefore, the ordered pair for x = 8 is (8, 2).
Complete table:
x, y | (x, y)
0 | (0, 0)
4 | (4, 1)
8 | (8, 2)
Find the equation of the line y = mx through the origin that describes the proportional relationship shown in the graph.
The coordinates are (4, 1), (8, 2)
To find the value of m for the line y = mx that passes through the origin and is proportional to the data given by the points (4, 1) and (8, 2), we can use the following proportionality equation:
y2 / y1 = x2 / x1
Substitute the x and y values from the given points:
2 / 1 = 8 / 4
2 = 2
Since the ratio of the y-values is equal to the ratio of the x-values, we know that the proportional relationship works.
Therefore, m = 1/4 as each unit increase in x leads to a 1/4 unit increase in y.
Hence, the equation of the line that describes the proportional relationship shown in the graph is:
y = 1/4x.
How about instead of the coordinates:
On the positive x and y axis there's Point 4 and Point 8
If the points (4, 4) and (8, 8) are on the positive x and y axis, this implies that the points are at the same location on both axes.
For a line passing through the origin and the points (4, 4) and (8, 8), it will satisfy the equation y = mx where m = 1. This is because the ratio of y to x is always 1 for these points, which indicates that they fall on the line y = x.
Therefore, the equation of the line that describes the proportional relationship in this case is y = x.