Mathematics, 23.07.2019 01:00 xJoel4199

The table represents a linear function. what is the slope of the function?

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Answer from: ashhull2002

-6

Step-by-step explanation:

The slope of a line is given with the formula

$m=\frac{y_2-y_1}{x_2-x_1}$

Using the first two points, (-2, 8) and (-1, 2), we have

m = (2-8)/(-1--2) = -6/(-1+2) = -6/1 = -6

Answer from: rickimmorgan

The slope of the given linear function is $\fbox{\begin\\\ \bf -6\\\end{minispace}}$ .

Further explanation:

The given table represents a linear function and is redrawn and attached below.

A linear function is defined as a function in which the degree or the highest power of the variable is .

The general form of linear function is, as follows:

$\fbox{\begin\\\ \math y=mx+c\\\end{minispace}}$

A linear function has one independent variable and one dependent variable. The independent variable is and the dependent variable is .

Here, is the constant term or the -intercept and is the slope that gives the rate of change of dependent variable.

The slope of the linear function is given by,

$\fbox{\begin\\\ \math m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\end{minispace}}$

From the attached table it is observed that the value of $x_{1},x_{2},x_{3},x_{4}\ \text{and}\ x_{5}$ are $-2,-1,0,1\ \text{and}\ 2$ respectively and the value of $y_{1},y_{2},y_{3},y_{4}\ \text{and}\ y_{5}$ are $8,2,-4,-10\ \text{and}\ -16$ respectively.

The slope $m_{1}$ can is calculated as,

$\begin{aligned}m_{1}&=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\&=\dfrac{2-8}{-1+2}\\&=\dfrac{-6}{1}\\&=-6\end{aligned}$

The slope $m_{2}$ is calculated as,

$\begin{aligned}m_{2}&=\dfrac{y_{3}-y_{2}}{x_{3}-x_{2}}\\&=\dfrac{-4-2}{0+1}\\&=\dfrac{-6}{1}\\&=-6\end{aligned}$

The slope $m_{3}$ is calculated as,

$\begin{aligned}m_{3}&=\dfrac{y_{4}-y_{3}}{x_{4}-x_{3}}\\&=\dfrac{-10+4}{1-0}\\&=\dfrac{-6}{1}\\&=-6\end{aligned}$

The slope $m_{4}$ is calculated as,

$\begin{aligned}m_{4}&=\dfrac{y_{5}-y_{4}}{x_{5}-x_{4}}\\&=\dfrac{-16+10}{2-1}\\&=\dfrac{-6}{1}\\&=-6\end{aligned}$

Since any two points from the attached table gives the same slope then all the points lie on a straight line.

Therefore, the slope of the function is $\fbox{\begin\\\ \bf -6\\\end{minispace}}$

Learn more:

1. A problem on slope-intercept form

2. A problem on center and radius of circle

3. A problem on circle

Answer details

Grade: Middle school

Subject: Mathematics

Chapter: Linear equations

Keywords: Linear equations, slope of a line, function, real numbers, ordinates, abscissa, interval, open interval, closed intervals, semi-closed intervals, semi-open intervals, sets, range domain, codomain, degree, highest power.

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