The Slope-Intercept form of the equation of the line is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
The slope can be found with:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Choose two points from the table. These could be the points (1,-4) and (4,-19). You can set up that:
[tex]\begin{gathered} y_2=-19 \\ y_1=-4 \\ x_2=4 \\ x_1=1 \end{gathered}[/tex]
Substituting values, you get that the slope of this line is:
[tex]m=\frac{-19-(-4)}{4-1}=-5[/tex]
You can substitute the slope and the first point into the equation in Slope-Intercept form:
[tex]-4=1(-5)+b[/tex]
Solve for "b":
[tex]\begin{gathered} -4+5=b \\ b=1 \end{gathered}[/tex]
Therefore, the Equation of this line in Slope-Intercept form is:
[tex]y=-5x+1[/tex]
