Rearrange the slope formula y = mx + b for the quantity of interest m. Make sure to show each step.

Answer 1

To rearrange the slope formula y = mx + b for the quantity of interest m, we need to isolate the term containing m on one side of the equation.

Step 1: Start with the slope formula y = mx + b.

Step 2: Subtract b from both sides of the equation to move it to the other side:
y - b = mx

Step 3: Divide both sides of the equation by x to isolate m:
(y - b)/x = m

So, the rearranged slope formula for the quantity of interest m is:
m = (y - b)/x

Answer 2

Dezeree received a $100 gift card and need new sweaters for school. The sweaters cost $27.50 each. Write an equation to determine how many sweaters she can buy and spend exactly $100, solve it, and determine if the value is a variable solution.

Answer 3

Let's define the number of sweaters Dezeree can buy as "s". We know that each sweater costs $27.50. The total amount she can spend is $100.

We can write an equation to represent this situation:
27.50s = 100

To solve this equation, we divide both sides by 27.50 to isolate the variable s:
s = 100/27.50

Evaluating the right side of the equation:
s ≈ 3.64

Since we can't have a fraction of a sweater, we need to round the result. Therefore, Dezeree can buy approximately 3 sweaters with $100.

It's important to note that the value of s is not a variable solution because it's not possible to buy a fraction of a sweater. The actual number of sweaters Dezeree can buy is 3.