Question

Which table represents a linear function?

Answer 1

Answer-

Only the first table represents a linear function.

Solution-

In order to be in linear function, the graph of the function must be a straight line.

Plotting the graph, by taking the data points from the given table and then plotting in the cartesian coordinates system, several graphs are generated. Among them only the 1st table, yields a straight line with a constant slope.

So, the 1st table represents a linear function, where x and y are in direct proportion with positive slope, hence when x increases, so does the y.

Answer 2

The table A is the correct option.

Further explanation:

The linear equation with slope m and y-intercept c is given as follows.

$\boxed{y = mx + c}$

Explanation:

Plot the points $\left( {1,\dfrac{1}{2}}\right),\left( {2,1} \right),\left( {3,1\dfrac{1}{2}} \right)$ and $\left( {4,2} \right)$ from the table 1

The graph of table 1 shows the linear function.

Plot the points $\left( {1,1} \right),\left( {2,\dfrac{1}{2}} \right),\left( {3,\dfrac{1}{3}} \right)$ and $\left( {4,2} \right)$ from the table 2.

The graph of table 2 shows that the function is not linear.

Plot the points $\left( {1,7} \right), \left( {2,9} \right), \left( {3,13} \right)$ and $\left( {4,21} \right)$ from the table 3.

The graph of table 3 shows that the function is not linear.

Plot the points $\left( {1,0} \right), \left( {2,6} \right), \left( {3,16} \right)$ and $\left( {4,30} \right)$ from the table 3.

The graph of table 3 shows that the function is not linear.

The table A is the correct option.

Kindly refer to the tables and the graph attached.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Linear equation

Keywords: numbers, slope, slope intercept, equation, linear equation, shaded region, y-intercept, graph, representation, origin, linear function.