To find the slope of the table, we need to use the next formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replace taking two points from the given table.
Then, P1(0,-3) and P2(1,-7):
[tex]m=\frac{-7-(-3)}{1-0}=\frac{-4}{1}=-4[/tex]Now, we can use the next equation to get the slope- intercept form:
[tex]y-y_1=m(x-x_1)[/tex]Relace using P(0,-3) and m-4.
Therefore:
[tex]\begin{gathered} y-(-3)=-4(x-0) \\ y+3=-4 \\ Solve\text{ for y to get the equation line:} \\ y=-4x-3 \end{gathered}[/tex]Finally, we get the slope-intercept form y=mx+b.
Where b represents the y-intercept.
The y-intercept is -3.
In conclusion:
Slope = -4
y-intercept b= -3
Formula h(x) = -4x-3