No.152 Finding a Linear Function from the Rate of Change
POINT
First find the slope from the rate of change, then substitute a given point into \(y=ax+b\) to find the y-intercept.
Example
1
The rate of change is \(3\), and \(y=5\) when \(x=2\). Find the linear function.
\(y=3x-1\)
2
When \(x\) increases by \(4\), \(y\) decreases by \(6\). Also, \(y=1\) when \(x=2\). Find the linear function.
\(y=-\frac32x+4\)
TRY
TRY 1
Rate of change \(2\); \(y=7\) when \(x=3\).
\(y=2x+1\)
TRY 2
Rate of change \(-3\); \(y=-5\) when \(x=2\).
\(y=-3x+1\)
TRY 3
When \(x\) increases by \(3\), \(y\) increases by \(6\); point \( (1,5) \).
\(y=2x+3\)
TRY 4
When \(x\) increases by \(4\), \(y\) decreases by \(2\); point \( (2,3) \).
\(y=-\frac12x+4\)