Solve the equation
2y = 6x + 2
Does the equation contain:
Infinite solutions
One solution
Zero Solutions
The given equation is in the form of a linear equation, which represents a straight line on a graph. To determine the number of solutions, we need to look at the slope of the line.
The equation can be rewritten as:
6x - 2y = -2
Dividing both sides of the equation by 2, we get:
3x - y = -1
Now, let's rewrite the equation in slope-intercept form:
y = 3x + 1
The slope of the line is 3, which means the line is not horizontal.
Since the line is not horizontal, it intersects with any horizontal line at only one point. Therefore, the equation has one solution.
for any old x you get a y
Therefore there are an infinite number of solutions.
eg
(0,1)
(1,4)
(2,7)
etc, etc, etc
You are correct. I apologize for the incorrect response. The given equation, 2y = 6x + 2, can be rewritten as y = 3x + 1. This is a linear equation with a slope of 3, which means that for every value of x, there is a corresponding value of y. Therefore, the equation has an infinite number of solutions. Thank you for pointing out the mistake.
To determine if the equation 2y = 6x + 2 contains infinite solutions, one solution, or zero solutions, we need to analyze the equation and its variables.
First, let's rearrange the equation to isolate the variable "y" on one side:
2y = 6x + 2
Divide both sides of the equation by 2:
y = 3x + 1
Now we have the equation in slope-intercept form (y = mx + b), where m represents the slope of the line and b represents the y-intercept.
By comparing this equation with the standard slope-intercept form y = mx + b, we can determine the slope and y-intercept of the line.
The equation 2y = 6x + 2 represents a linear equation with a slope of 3 and a y-intercept of 1.
From this information, we conclude that the equation represents a straight line on a coordinate plane.
Since a straight line has infinite points, the equation 2y = 6x + 2 has infinite solutions.
To solve the equation 2y = 6x + 2, we can start by isolating y.
Step 1: Divide both sides of the equation by 2 to get y by itself:
2y/2 = (6x + 2)/2
y = 3x + 1
Now that we have the equation in the form y = mx + b, where m is the slope and b is the y-intercept, we can determine the number of solutions based on the slope.
In this case, the equation is in slope-intercept form, which means it represents a straight line. The equation y = 3x + 1 has a slope of 3, which means the line is upward sloping.
Based on the slope, we can determine the number of solutions:
1. One solution: If the line intersects the x-axis at only one point, the equation has one solution. In other words, the line is not parallel to the x-axis, and it intersects the x-axis at one unique point.
2. Infinite solutions: If the line is parallel to the x-axis, it will never intersect with the x-axis. This means that any value of x will result in a valid solution for y. In this case, the equation has infinite solutions.
3. Zero solutions: If the line is parallel to the y-axis, it will not intersect the x-axis at any point. In this case, the equation has zero solutions.
To determine which case applies to the equation y = 3x + 1, we can look at its slope. Since the slope is not zero or undefined (parallel to the x or y-axis), the equation has one solution.
Therefore, the equation 2y = 6x + 2 contains one solution.