Relations and functions
y=-3/4x+4
and
y=2(x)
state weather each equation is a function
state shape and location on the graph
that's "whether" not "weather".
visit wolframalpha.com and just type in a function. It will show you the graph and other information. Be sure to note how interprets you input. You may need to use some parentheses to ensure proper evaluation.
The graph represents a function if no vertical line crosses the graph more than once.
To determine whether each equation is a function, we need to check if each x-value is paired with only one y-value.
1. Equation: y = -3/4x + 4
To determine whether this equation is a function, we need to check if for any given x-value, there is only one corresponding y-value. We can rearrange the equation in the standard form of y = mx + b, where m represents the slope and b represents the y-intercept:
y = (-3/4)x + 4
Since the slope (-3/4) is not zero, each x-value will have a unique y-value. Therefore, this equation is a function.
To illustrate its shape and location on the graph, we can plot some points. We can choose arbitrary values for x and find the corresponding y-values. Let's choose x = 0, 1, and 2:
When x = 0, y = (-3/4)(0) + 4 = 4. So, one point is (0, 4).
When x = 1, y = (-3/4)(1) + 4 = 3 + 4 = 7. So, another point is (1, 7).
When x = 2, y = (-3/4)(2) + 4 = -6/4 + 4 = -3/2 + 4 = 5/2. So, one more point is (2, 5/2).
Plotting these points and connecting them, you will find a straight line on the graph that slants downward from left to right, intersecting the y-axis at the point (0, 4).
2. Equation: y = 2x
Similar to the first equation, we can rearrange this equation to the form y = mx + b:
y = 2x
Again, the slope (2) is not zero, so each x-value will have a unique y-value, making this equation a function.
To illustrate its shape and location on the graph, we can again plot some points. Choosing x = 0, 1, and 2:
When x = 0, y = 2(0) = 0. Thus, one point is (0, 0).
When x = 1, y = 2(1) = 2. So, another point is (1, 2).
When x = 2, y = 2(2) = 4. One more point is (2, 4).
Plotting these points and connecting them, you will find a straight line on the graph that passes through the origin (0, 0) and has a positive slope, slanting upward from left to right.
In summary:
- The first equation, y = -3/4x + 4, is a function. It represents a downward slanting straight line on the graph that intersects the y-axis at the point (0, 4).
- The second equation, y = 2x, is also a function. It represents an upward slanting straight line passing through the origin (0, 0).