Final answer:
To find the value of k so that the line through the points (4, -3) and (k, 5) is perpendicular to the line 3y + 2x = 6, we need to find the slope of the given line and then find the negative reciprocal of that slope. The value of k is 11.
Step-by-step explanation:
To find the value of k so that the line through the points (4, -3) and (k, 5) is perpendicular to the line 3y + 2x = 6, we need to find the slope of the given line and then find the negative reciprocal of that slope.
The given line can be rewritten in the form y = mx + b, where m is the slope. Rearranging the equation gives us y = (-2/3)x + 2.
The slope of the given line is -2/3. The negative reciprocal of this slope is 3/2.
Therefore, the line through the points (4, -3) and (k, 5) is perpendicular to 3y + 2x = 6 when the value of k is 11.