Question

Which equation could represent the relationship between x and y in the T-chart shown below?

Answer 1

Step-by-step explanation:

The equation of a line is:

`y=mx+b`

Where m is the slope and b is the y-intercept.

To find the equation from the T-chart we can pick two rows, replace x and y and solve a system of equations for m and b.

Another way is to put the values of the chart into the equations from the options and see which one is true for all values:

y = x+2:

`\begin{gathered} 3=1+2 \\ 3=3\text{ }\rightarrow\text{ true} \\ 7=2+2 \\ 7=4\text{ }\rightarrow\text{ false} \\ 11=3+2 \\ 11=5\text{ }\rightarrow\text{ false} \end{gathered}`

y = 4x - 1:

`\begin{gathered} 3=4\cdot1-1 \\ 3=3\text{ }\rightarrow\text{ true} \\ 7=4\cdot2-1 \\ 7=7\text{ }\rightarrow\text{ true} \\ 11=4\cdot3-1 \\ 11=11\text{ }\rightarrow\text{ true} \end{gathered}`

This is the equation that represents the relation from the T-chart.

Answer:

y = 4x - 1