Determine whether the line with equation 2x+ 3y + 4 = 0 is parallel to the line through the points with coordinates (9, 4) and (3, 8).
Parallel means that the lines have the same gradient/slope. For example, the lines in an equal sign are parallel.Consider the standard equation of a line is: y = mx + c where m is the gradient. Rewriting our equation gives us 2x + 3y +4 = 0 --> 3y = -2x -4 ----> y = -(2/3)x -(4/3c)From this standard form we see clearly the line has a slope of -2/3.Then we use the equation of finding the gradient of a line through two points: m = (y2 - y1)/( x2 - x1). Inputting the values we have we obtain m = (8-4)/(3-9) = 4/-6 = -2/3. We observe that the gradient of the lines are the same and therefore the lines are parallel
