Suggested languages for you:

Americas

Europe

Q. 4

Expert-verifiedFound in: Page 173

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

In Problems 4 and 5, determine whether the function is linear or nonlinear. If the function is linear, find the equation of the line.

The function is linear and the equation of the line is $y=5x+3$.

Determine whether the function is linear or nonlinear. If the function is linear, find the equation of the line.

The linear function is given by

$g\left(x\right)=mx+b;m\ne 0$

The slope of the graph is *m *and the y-intercept is *b. *The average rate of change is equal to the slope.

localid="1646321689835" $m=\frac{g\left({x}_{2}\right)-g\left({x}_{1}\right)}{{x}_{2}-{x}_{1}}$

The linear function have a constant average rate of change.

Look at the given table and notice that

${y}_{5}-{y}_{4}={y}_{4}-{y}_{3}={y}_{3}-{y}_{2}={y}_{2}-{y}_{1}=5$.

When you changes x value for 1. So, average rate of change is constant. Then the slope is $m=5$.

Also the y-intercept is $b=3$ because that is the value of the function for $x=0$.

Then the equation of function is:

$f\left(x\right)=5x+3$

The function is linear and the equation of line is $f\left(x\right)=5x+3$.

In Problems 21–28, determine whether the given function is linear or nonlinear. If it is linear, determine the equation of the line .

x | $y=f\left(x\right)$ |

-2 | 4 |

-1 | 1 |

0 | -2 |

1 | -5 |

2 | -8 |

94% of StudySmarter users get better grades.

Sign up for free