Question

Two different functions are represented by this graph and this table:A. Image result for linear graph B. Image result for x-y table linear equationWhich linear function has a greater slope?

Answer 1

A linear equation is represented by the general form:

$\begin{gathered} y\text{ = mx + c} \\ \text{where m is the slope} \end{gathered}$

Required: We derive the equation using the given data and then compare their slopes

First, the graph has the following parameters

$\begin{gathered} \text{Slope (m) = }\frac{5\text{ - (-1)}}{1\text{ - (-2)}} \\ =\text{ }\frac{5+\text{ 1}}{1\text{ + 2}} \\ =\text{ 3} \\ y-\text{ intercept (c) = 3} \end{gathered}$

For the table, we pick two points/row data and then find the slope (m)

Let's use the first and second points i.e

$(0,1)\text{ and (1,4)}$

The equation to find the slope given two points is given as

$\begin{gathered} m_{}\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}$

By substituting:

$\begin{gathered} m\text{ = }\frac{4\text{ - 1}}{1\text{ -0}} \\ m\text{ = }\frac{3}{1} \\ m\text{ =3 } \\ \end{gathered}$

Check: Which linear function has a greater slope?

Answer: none

Reason: slope for the equation represented by the graph is the same as that for the table.