The slope-intercept form of the equation of a line, is:
[tex]y=mx+b[/tex]Where m, the coefficient of x, is the slope of the line, and b, the constant term, is the y-intercept.
To find the slope of the line, substitute the corresponding values of x and y into the slope formula. Use, for instance, the points (-8,-42) and (6,28):
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{(28)-(-42)}{(6)-(-8)} \\ =\frac{28+42}{6+8} \\ =\frac{70}{14} \\ =5 \end{gathered}[/tex]The y-intercept equals the value of y when x=0. From the table, we can see that the y-intercept is equal to -2.
Substitute m=5 and b=-2 to find the equation of the line described by the table.
Therefore, requested the equation in slope-intercept form, is:
[tex]y=5x-2[/tex]