Final answer:
The slope of the given line 3x+2y=8 is -3/2, and the slope of Line D, being perpendicular, is the negative reciprocal, 2/3. Using the point (3,4) and the slope-point formula, the equation of Line D is found to be y = (2/3)x + 2.
Step-by-step explanation:
To find the equation of line D which is perpendicular to the line with equation 3x + 2y = 8, we first need to find the slope of the given line. We can rewrite the equation in slope-intercept form, which is y = mx + b where m is the slope and b is the y-intercept. By rearranging the given equation we get y = -3x/2 + 4. The slope of this line is -3/2. Since line D is perpendicular to this line, its slope would be the negative reciprocal of -3/2, which is 2/3.
Now that we have the slope of line D, we use the point-slope formula, y - y1 = m(x - x1), where (x1, y1) is a point on the line (which is (3,4)) and m is the slope of the line. Substituting the point and the slope into the formula gives us y - 4 = (2/3)(x - 3). Simplifying this equation by distributing and then moving all terms to one side gives us the final equation of line D in slope-intercept form: y = (2/3)x + 2.