Find the slope of a line perpendicular to each given line.
Y = -1/2x - 2
y + 7 = 5/2(4x + 6)
?
The given line is in slope-intercept form, y = mx + b, where m is the slope. Therefore, the slope of the given line is -1/2.
To find the slope of a line perpendicular to the given line, we take the negative reciprocal of the slope. So, the slope of a line perpendicular to y = -1/2x - 2 is 2/(-1/2) = -4.
For the second equation, y + 7 = 5/2(4x + 6), we can distribute the 5/2 to get y + 7 = 20x + 15. Then, we can rearrange the equation to slope-intercept form, y = 20x + 15 - 7, which simplifies to y = 20x + 8.
Again, the slope of the given line is 20. The slope of a line perpendicular to this line would be the negative reciprocal of 20, which is -1/20.