Mathematics, 23.06.2019 10:10 Braxton12

Line ab passes through points a(–6, 6) and b(12, 3). if the equation of the line is written in slope-intercept form, y = mx + b, then m = – and b =

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Answer from: IsaacRodriguez245

In summary, m = -1/6 and b = 5

Step-by-step explanation:

As we move from A(–6, 6) to B(12, 3), x increases by 18 and y decreases by 3. Thus, the slope of Line AB is m = rise / run = -3 / 18, or m = -1/6.

Let's make use of the slope-intercept formula to find the value of b:

y = mx + b becomes 3 = (-1/6)(12) + b, or

3 = -2 + b

Then b must be 5.

In summary, m = -1/6 and b = 5, and the equation of Line AB is y = (-1/6)x + 5.

Answer from: Quest

(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

Answer from: Quest

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

$m=y/x=1/3$

the equation of the dashed line is

$y=(1/3)x$

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

$y> (1/3)x$

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

$m=(4-0)/(0-4)=-1$

the equation of the solid line is

$y=-x+4$

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

$y\leq-x+4$

step 3

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

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Line ab passes through points a(–6, 6) and b(12, 3). if the equation of the line is written in slope...