instrctions:graph each linear equation .tell whether it represents a function.
1.) x+y=4
HELP QUICK PLEEZE!!!!!!!!!!!!!!!!!!!!!
x = -y+4
y = -x+4
without graphing tell whether each point is on the graph of y=-4x-1.
(1/2,-1)
To graph the linear equation x + y = 4 and determine if it represents a function, follow these steps:
Step 1: Convert the equation to slope-intercept form (y = mx + b).
Rearrange the equation to solve for y:
y = 4 - x
Step 2: Create a table of values for x and y.
Choose a few values for x, substitute them into the equation, and solve for y. For example, let's choose x = 0, 1, and 2:
For x = 0:
y = 4 - 0
y = 4
So, the first point is (0, 4).
For x = 1:
y = 4 - 1
y = 3
The second point is (1, 3).
For x = 2:
y = 4 - 2
y = 2
The third point is (2, 2).
Step 3: Plot the points on a graph.
Plot the points on a coordinate plane. The x-coordinate represents the values of x from the table, and the y-coordinate represents the values of y from the table. In this case, the points are (0, 4), (1, 3), and (2, 2).
Step 4: Draw a line through the points.
Connect the plotted points using a straight line. In this case, the line should pass through (0, 4), (1, 3), and (2, 2).
Step 5: Determine if the graph represents a function.
A function is a mathematical relation where each input (x-value) corresponds to exactly one output (y-value). To determine if the graph represents a function, examine if the vertical line intersects the graph at more than one point for any given x-value. If the vertical line intersects the graph at multiple points, the graph doesn't represent a function. Otherwise, it does.
In this case, when you draw a vertical line through the graph of x+y=4, it will intersect the line at only one point for any given x-value. Hence, the graph represents a function.
I hope this helps! Let me know if you have any further questions.