X * 1.085 = 19.18
solve for x

Why is this how you figure it out? well... you have the price of the CD cover and the total is the price of the CD cover with tax.

Price of the CD cover would be: x * 1 = price of cd cover
Put that tax on there: x * 1.085 = price of cd cover with tax

why .085? move that decimal over two places to the left from the 8.5%

3 0

3 years ago

Write the equation of the line that passes through

Gnom [1K]

Answer:

$y=\frac{\displaystyle 1}{\displaystyle 7}x+\frac{\displaystyle15}{\displaystyle 7}$

Step-by-step explanation:

Hi there!

Slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

$m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}$ where two given points are $(x_1,y_1)$ and $(x_2,y_2)$

Plug in the given points (-1, 2) and (6, 3):

$m=\frac{\displaystyle 3-2}{\displaystyle 6-(-1)}\\\\m=\frac{\displaystyle 3-2}{\displaystyle 6+1}\\\\\m=\frac{\displaystyle 1}{\displaystyle 7}$

Therefore, the slope of the line is $\frac{\displaystyle 1}{\displaystyle 7}$ . Plug this into $y=mx+b$ :

$y=\frac{\displaystyle 1}{\displaystyle 7}x+b$

2) Determine the y-intercept (b)

$y=\frac{\displaystyle 1}{\displaystyle 7}x+b$

Plug in one of the given points and solve for b:

$2=\frac{\displaystyle 1}{\displaystyle 7}(-1)+b\\2=-\frac{\displaystyle 1}{\displaystyle 7}+b$

Add $\frac{\displaystyle 1}{\displaystyle 7}$ to both sides to isolate b:

$2+\frac{\displaystyle 1}{\displaystyle 7}=-\frac{\displaystyle 1}{\displaystyle 7}+b+\frac{\displaystyle 1}{\displaystyle 7}\\\\\frac{\displaystyle15}{\displaystyle 7} =b$

Therefore, the y-intercept of the line is $\frac{\displaystyle15}{\displaystyle 7}$ . Plug this back into $y=\frac{\displaystyle 1}{\displaystyle 7}x+b$ :

$y=\frac{\displaystyle 1}{\displaystyle 7}x+\frac{\displaystyle15}{\displaystyle 7}$

I hope this helps!

3 0

3 years ago