Answer:
13. The slope for a line that is perpendicular to the line y=4x+8 is -1/4
14. The slope for a line that is perpendicular to the line x=-6 is 0
15. The equation for a line that is perpendicular to the line 8x-4y=12 and passes through the origin is y = - (1/2) x
16. The equation for a line that is perpendicular to the line y=-(1/3)x and passes through the point (0,-10) is y=3x-10
Step-by-step explanation:
13. What is the slope for a line that is perpendicular to the line y=4x+8?
y=mx+b
Comparing with the form slope-intercept, the slope of the given line is the coefficient of x, then the slope of the given line is 4.
A line perpendicular to y=4x+8 must have a slope opposite and inverse, then:
Slope of the perpendicular = - 1/4
14. What is the slope for a line that is perpendicular to the line x=-6?
The line x=-6 is a vertical line. A line perpendicular to the line x=-6 must be a horizontal line (Angle=0°), then:
Slope of the perpendicular = tan Angle = tan 0° = 0
15. Write the equation for a line that is perpendicular to the line 8x-4y=12 and passes through the origin.
8x-4y=12
Isolating y: Subtracting 8x both sides of the equation:
8x-4y-8x=12-8x
-4y=-8x+12
Dividing all the terms by -4:
-4y/(-4)= -8x/(-4)+12/(-4)
y=2x-3
The slope of the given line is 2
The slope of the perpendicular is m=-1/2 (opposite and inverse to the slope of the given line)
The perpendicular passes through the origin:
P1=(0,0)=(x1,y1)→x1=0, y1=0
Using the equation point - slope:
y-y1=m(x-x1)
Replacing the known values:
y-0=(-1/2)(x-0)
y=(-1/2)x
16. Write an equation for a line that is perpendicular to the line y=-(1/3)x and passes through the point (0,-10).
The slope of the given line is -(1/3)
The slope of the perpendicular is m=3/1→m=3 (opposite and inverse to the slope of the given line)
The perpendicular passes through the point:
P1=(0,-10)=(x1,y1)→x1=0, y1=-10
Using the equation point - slope:
y-y1=m(x-x1)
Replacing the known values:
y-(-10)=3(x-0)
y+10=3x
Isolating y: Subtracting 10 both sides of the equation:
y+10-10=3x-10
y=3x-10
