Question 1
Examine the equation that follows:
4. 2y=6x+2
determine how this equation forms a system
with one solution, no solution, or infinite solutions.
a. Solve equation and make sure it is in y=mx+b format.
b. Graph equation on the coordinate grid and label it.
a. To solve the equation 2y=6x+2 for y in the form y=mx+b, we first isolate y by dividing both sides by 2:
2y = 6x + 2
y = 3x + 1
Therefore, the equation in y=mx+b format is y = 3x + 1.
b. To graph the equation y=3x+1 on the coordinate grid, we can start by plotting the y-intercept, which is 1.
Next, we can use the slope of 3 to find another point. This means that for every unit we move to the right, we move up 3 units.
We can plot another point at x=1, y=4.
Now we can draw a straight line through these two points to represent the equation y=3x+1. Label the line as "y=3x+1".
This equation forms a system with one solution, as it is a linear equation with a unique solution for every value of x.