Question

What is the answer to 7 or 8???

Answer 1

7. parallel: k = 3

perpendicular: k = -4/3

8. $1300

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=\frac32x+\frac34`

4y = k(2x + 10)

⇒ 4y = 2kx + 10k

⇒
`y = \frac12kx + \frac52k`

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

`\implies \frac32=\frac12k`

`\implies k=3`

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

`\implies \frac32 * \frac12k=-1`

`\implies \frac12k=-\frac23`

`\implies k=-\frac43`

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=(y_2-y_1)/(x_2-x_1)=(195-110)/(20-10)=(17)/(2)`

Now use the point-slope form of linear equation:

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

`\implies y-110=(17)/(2)(x-10)`

`\implies y=(17)/(2)x+25`

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

`\implies y=(17)/(2)(150)+25=1300`

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