Find the slope of a line perpendicular to each given line.
Y = -1/2x - 2
y + 7 = 5/2(4x + 6)
To find the slope of a line perpendicular to a given line, you need to find the negative reciprocal of the slope of the given line.
1) Given line: y = -1/2x - 2
The slope of this line is -1/2.
The negative reciprocal of -1/2 is 2.
Therefore, the slope of a line perpendicular to y = -1/2x - 2 is 2.
2) Given line: y + 7 = 5/2(4x + 6)
First, rewrite the equation in slope-intercept form:
y + 7 = 5/2 * 4x + 5/2 * 6
y + 7 = 10x + 15
y = 10x + 8
The slope of this line is 10.
The negative reciprocal of 10 is -1/10.
Therefore, the slope of a line perpendicular to y + 7 = 5/2(4x + 6) is -1/10.