determine the equation of a line in slope-intercept parallel to 6x+2y=19 and passing through (-6,-13).

Answer:[tex]y = - 3x - 31[/tex]Step-by-step explanation:By definition, the slopes of parallel lines are equal. Thus, we need to first five the slope of 6x+2y=19. Recall that slope intercept form is[tex]y = mx + b[/tex]where m is the slope and b is the y-intercept. So, to find the slope of 6x+2y=19, put it on slope intercept form like so:6x+2y=196x-19=-2y-3x+19/2=ySo the slope of the line is -3. Then, we will use point slope form to find the equation of the parallel line that passes through (-6, -13). Recall that point slope form isy-y1=m(x-x1). Using this we find the equation of the parallel line to be:y+13=-3(x+6)y+13=-3x-18y=-3x-31Thus, the slope of the parallel line is y=-3x-31.I hope this helps! Cheers!