Question

What is the answer to 7 or 8???

Answer 1

Answer:

7. parallel:  k = 3

   perpendicular:  k = -4/3

8. $1300

Step-by-step explanation:

7.

Rewrite each equation as the slope-intercept form of a linear equation:

y = mx + b (where m is the slope and b is the y-intercept)

  8y = 12x + 6

⇒ $y=\dfrac32x+\dfrac34$

   4y = k(2x + 10)

⇒ 4y = 2kx + 10k

⇒ $y = \dfrac12kx + \dfrac52k$

If the graphs are parallel their slopes will be the same.

$\implies \dfrac32=\dfrac12k$

$\implies k=3$

If the graphs are perpendicular then the product of their slopes will be -1.

$\implies \dfrac32 \times \dfrac12k=-1$

$\implies \dfrac12k=-\dfrac23$

$\implies k=-\dfrac43$

8. Create a linear equation, where x is the number of coffee mugs and y is the total cost (in dollars).

Choose 2 ordered pairs from the table:  (10, 110) and (20, 195)

Let $(x_1,y_1)$ = (10, 110)

Let $(x_2,y_2)$ = (20, 195)

Use the slope formula to find the slope m:

$\implies m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{195-110}{20-10}=\dfrac{17}{2}$

Now use the point-slope form of linear equation:

$\implies y-y_1=m(x-x_1)$

$\implies y-110=\dfrac{17}{2}(x-10)$

$\implies y=\dfrac{17}{2}x+25$

Substitute x = 150 into the equation and solve for y:

$\implies y=\dfrac{17}{2}(150)+25=1300$

Therefore, the total cost of ordereing 150 mugs is $1300