X=8

THE DIRECTIONS ARE ON THE TOP

y = 40

Step-by-step explanation:

For #7, we are told that y = 10 when x = 2

We are also told that 'y varies directly as x'. That means there is some constant number, k, so that

Formula -->  y = kx

Since y=10 and x= 2, we substitute those numbers into the formula.

We get 10 = k × 2.  

So k has to be 5, right?

k = 5

So what is y when x = 8?

Use the formula.

y=kx ---> That gives us y = k × 8. But we know k is 5.

                                 So y = 5 × 8 = 40

                                       y = 40

9514 1404 393

  7. y = 5x; y = 40

  8. y = 1/3x; y = 8/3

Step-by-step explanation:

In the direct proportion equation y=kx, the value of k can be found as ...

  k = y/x . . . . . divide both sides by x to solve for k

__

7. k = 10/2 = 5

The equation is ...

  y = 5x

For x=8, the value of y is found using the equation:

  y = 5(8) = 40

__

8. Same deal, different numbers.

  k = 6/18 = 1/3

  y = 1/3x . . . . . the equation

  y = 8/3 . . . . . y for x=8

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be