Find the slope of a line perpendicular to each given line.
—x = 6 — Зу

  -3

Step-by-step explanation:

Solve the equation for y to find the slope of the given line:

  1/3x = -2 +y . . . . . divide by -3

  y = 1/3x +2 . . . . . the slope is 1/3. (The slope is the coefficient of x.)

The perpendicular line will have a slope that is the negative reciprocal of this:

  desired slope = -1/(1/3) = -3

The perpendicular line has a slope of -3.

Comment on the solution

You may have noticed that when x and y are on opposite sides of the equal sign, the slope is the coefficient of x when the coefficient of y is 1. We don't actually need to move the constant in order to identify the slope of the given line.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3