We can take any 2 points both from x and y and use the equation of a line formula to find out the equation of the line represented by the points in the table.
Let's take the points:
[tex]\begin{gathered} (x_1,y_1)=(0,-5) \\ (x_2,y_2)=(1,4) \end{gathered}[/tex]
The equation of a line formula is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Let us plug in the points into this formula and do a little algebra to re-arrange the equation in the slope-intercept form, which is y = mx + b. The steps are shown below:
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-(-5)=\frac{4-(-5)}{1-0}(x-0) \\ y+5=\frac{4+5}{1}(x) \\ y+5=\frac{9}{1}(x) \\ y+5=9x \\ y=9x-5 \end{gathered}[/tex]
The slope-intercept form is given by:
[tex]y=9x-5[/tex]
Where 9 is the slope and -5 is the y-intercept (y-axis cutting point)
