The equation of the line passing through the points (6, 9) and (4, 17) can be expressed as y = mx + b. give the value of b

slope = (17 - 9)/(4 - 6) = 8/-2 = -4

y = mx + b

b = y - mx

b = 9 - (-4)(6)

b = 9 + 24

b = 33

equation

y = -4x + 33

answer

b = 33

equation: y = -4x + 33

(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

d

gimmee one of those gold crowns!

~coco