Question
Fill in the blanks to explain how to find the rate of change and the y-intercept from a table.
If the y-intercept is not in a table, extend the pattern so that the table now includes an input-output pair where________
1: y=0, (0,0), x=0, x=y
If the y-intercept is not in a table, extend the pattern so that the table now includes an input-output pair where________
1: y=0, (0,0), x=0, x=y
Answers
GPT-4o mini
To find the rate of change and the y-intercept from a table, follow these steps:
If the y-intercept is not in a table, extend the pattern so that the table now includes an input-output pair where **x = 0**. This means you are looking for the value of y when the input (x) is zero. This value of y will give you the y-intercept of the linear equation.
To find the rate of change, you can determine the change in y divided by the change in x between two points in the table. The formula for the rate of change (slope) is:
\[ \text{Rate of Change} (m) = \frac{\text{Change in } y}{\text{Change in } x} = \frac{y_2 - y_1}{x_2 - x_1} \]
where (x1, y1) and (x2, y2) are any two points in the table.
By finding the y-intercept (where x = 0) and calculating the rate of change using the points you have, you can effectively determine the equation of the line represented by the data in the table.
If the y-intercept is not in a table, extend the pattern so that the table now includes an input-output pair where **x = 0**. This means you are looking for the value of y when the input (x) is zero. This value of y will give you the y-intercept of the linear equation.
To find the rate of change, you can determine the change in y divided by the change in x between two points in the table. The formula for the rate of change (slope) is:
\[ \text{Rate of Change} (m) = \frac{\text{Change in } y}{\text{Change in } x} = \frac{y_2 - y_1}{x_2 - x_1} \]
where (x1, y1) and (x2, y2) are any two points in the table.
By finding the y-intercept (where x = 0) and calculating the rate of change using the points you have, you can effectively determine the equation of the line represented by the data in the table.