• Given the table of values, you can identify these points:
[tex](0,4),(1,8),(2,12),(3,16),(5,24),(6,28),(7,32)[/tex]
If you plot them on a Coordinate Plane, you get:
As you can observe, it is a Linear Function.
• The equation of a line in Slope-Intercept Form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
In this case, you can identify in the graph that:
[tex]b=4[/tex]
Therefore, you can substitute that value and the coordinates of one of the points on the line, into this equation:
[tex]y=mx+b[/tex]
And then solve for "m", in order to find the slope of the line.
Using this point:
[tex](1,8)[/tex]
You get:
[tex]\begin{gathered} 8=m(1)+4 \\ 8-4=m \\ m=4 \end{gathered}[/tex]
Therefore, the equation for the data in Slope-Intercept Form is:
[tex]y=4x+4[/tex]
Hence, the answer is:
• It represents a Linear Function.
,
• Equation:
[tex]y=4x+4[/tex]
