Hello, Anna,
I don't see a question in the problem you stated, but I'll assume you want the equation that will match the data in the table, in the format of the equation included.
The form y = mx + b, which is how y = 3x + 1 is written, is called slope-intercept form, and is a common way to write equations of a straight line. That is because the "m" is the equation is called the slope of the line. The slope of y = 3x + 1 is 3. The "b" is the y intercept, the value of y when x = 0. In the example, y = 1 when x = 0.
The slope of a line is the rate at which x increases as y increases. It is also called the "Rise over the Run," a term that reminds us that we can calculate the slope by measure the change in y (the rise) and divide by the corresponding change in x (the run).
I found the slope by by taking the change in x and y for the first two points. The change in y (6-2=4) divided by the change in x (-2-(-3)=1). Y is the rise, x is the run, so y/x = the slope, (4/1) or 4, in this case.
The equation then looks like this:
y = 4x + b
To find b, use one of the data points and solve for b:
Let's use point (-3,2):
2 = 4*(-3) + b
b = 2 +12
b = 14
The equation is y = 4x + 14
Use this equation to solve for the values of x to see if y matches the values provided. We can see they do:
Robert S.
01/15/21
Anna T.
Thank you very much. It was really helpful and easy to follow.01/15/21