Final answer:
The equation of line m is y = 3x - 2, using the given point and y-intercept. Line n is perpendicular to m, thus its slope is -1/3. After using its x-intercept to determine the y-intercept, the equation of line n is y = (-1/3)x + 2.
Step-by-step explanation:
The equation of a straight line is given by y = mx + b, where m is the slope of the line and b is the y-intercept. Given line m passes through the point (-2, 4) and has a y-intercept of -2, we first find its slope m using the formula for slope between two points: (4 - (-2)) / (-2 - 0), giving us a slope of 3. Hence, the equation for line m is y = 3x - 2. Since line n is perpendicular to line m, its slope will be the negative reciprocal of line m's slope, which is -1/3. Knowing the x-intercept of line n is at x = 6, we can determine its y-value to be 0 at this point. By plugging the slope and the x-intercept into the equation, we have y = (-1/3)x + b. Substituting x = 6 and y = 0 to find b, we get 0 = (-1/3)(6) + b, resulting in b = 2. Therefore, the equation of line n is y = (-1/3)x + 2.