Final answer:
To find the values of l and m in the equation 4x-ly=m, we can use the fact that the given line is perpendicular to another line and intersects at a point. By comparing the slopes of the lines, we can determine the value of l. Then, substituting this value into the equation and using the given point of intersection, we can solve for m.
Step-by-step explanation:
To find the values of l and m in the equation 4x-ly=m, we need to determine the slope of the line represented by the equation and use the fact that it is perpendicular to the line 4x-3y=10.
First, we can rewrite the equation 4x-ly=m as y = (4x-m)/l. The slope of this line can be determined by comparing it to the general form of a linear equation, y = mx + b, where m is the slope. In this case, the slope is (4/l).
Since the lines represented by the given equations are perpendicular, their slopes are negative reciprocals. Therefore, the slope of the line 4x-3y=10 is (-4/3). Setting the slopes equal to each other and solving for l, we have:
4/l = -4/3
Cross multiplying, we get:
4 * 3 = -4l
Simplifying, we find:
12 = -4l
Dividing both sides by -4, we get:
l = -3
Substituting this value of l into 4x-ly=m and using the point (4,2) where the lines intersect, we can solve for m:
4x - (-3)y = m
4x + 3y = m
Substituting x=4 and y=2:
4(4) + 3(2) = m
Simplifying, we find that m = 22.