Question

Line 1: 3x + 4y = -14 represents the graph. Line 2, passing through (-5,7) and perpendicular to Line 1, is represented by y=mx+b. Find m+b.

a) -13
b) -11
c) -9
d) -7

Answer 1

To find the slope of Line 2, we first find the slope of Line 1, which is -3/4. Perpendicular lines have slopes that are negative reciprocals, so Line 2 has a slope of 4/3. After substituting the given point in the equation y = mx + b, we find that b = 41/3. Adding the slopes of Line 2 and the y-intercept, we get 15. None of the option is correct

Step-by-step explanation:

To find the slope of Line 2, which is perpendicular to Line 1, we first need to find the slope of Line 1. The slope-intercept form of a line is y = mx + b, where m is the slope. Line 1 is given by 3x + 4y = -14, so we rearrange it into the slope-intercept form as y = -(3/4)x - 14/4. The slope of Line 1 is -3/4. Perpendicular lines have slopes that are negative reciprocals of each other, so the slope of Line 2 is 4/3.

Next, we substitute the given point (-5,7) into the equation y = mx + b and solve for b. This gives us 7 = (4/3)(-5) + b. Simplifying the equation, we have 7 = -20/3 + b. To isolate b, we add 20/3 to both sides and get b = 41/3.

Finally, we find m + b by adding the slopes of Line 2 and the y-intercept b. m + b = 4/3 + 41/3 = 45/3 = 15. Therefore, the answer is 15.

None of the option is correct