Question
Write the equation of the function if its rate of change is negative 6, and its initial value is 11.
Answers
GPT-4o mini
To write the equation of a linear function given its rate of change (slope) and initial value (y-intercept), we can use the slope-intercept form of a linear equation, which is:
\[ y = mx + b \]
where:
- \( m \) is the slope (rate of change),
- \( b \) is the y-intercept (initial value).
Given:
- Rate of change (\( m \)) = -6
- Initial value (\( b \)) = 11
Substituting these values into the slope-intercept form, we get:
\[ y = -6x + 11 \]
So the equation of the function is:
\[ y = -6x + 11 \]
\[ y = mx + b \]
where:
- \( m \) is the slope (rate of change),
- \( b \) is the y-intercept (initial value).
Given:
- Rate of change (\( m \)) = -6
- Initial value (\( b \)) = 11
Substituting these values into the slope-intercept form, we get:
\[ y = -6x + 11 \]
So the equation of the function is:
\[ y = -6x + 11 \]