Solution:
The slope-intercept for a line with slope m and y-intercept b is given by the following equation:
[tex]y\text{ = mx + b}[/tex]now, to find the slope m of a line that passes through the points (-8 -15) and (14 -15), we can use the following equation:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}[/tex]where (X1,Y1) and (X2,Y2) are given points on the line. In this case, we have the points:
(X1,Y1) = (-8,-15)
(X2.Y2) = (14,-15)
now, replacing these points into the slope-equation, we get:
[tex]m\text{ = }\frac{-15+15}{14+8}\text{ = 0}[/tex]thus, the given line can be expressed as a constant function. That is, the provisional equation of the given line is:
[tex]y\text{ = (0)x+b}[/tex]this is equivalent to:
[tex]y\text{ = b}[/tex]to find b, we can replace any point on the line into the previous equation, for example, the point (x,y) = (14,-15) to obtain:
[tex]y\text{ = }-15[/tex]we can conclude that the line equation of the given line is:
[tex]y\text{ = -15}[/tex]