Rearrange the slope formula y = mx + b for the quantity of interest m. Make sure to show each step.
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
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.
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.
To rearrange the slope formula, y = mx + b, for the quantity of interest m, we need to isolate m on one side of the equation. Here are the steps to do that:
Step 1: Start with the given equation: y = mx + b.
Step 2: Subtract b from both sides of the equation to separate mx on one side: y - b = mx.
Step 3: Divide both sides of the equation by x to solve for m: (y - b) / x = m.
Therefore, the rearranged slope formula for the quantity of interest m is: m = (y - b) / x.
To rearrange the slope formula y = mx + b for the quantity of interest m, we'll isolate m on one side of the equation. Here's how you can do it step by step:
Step 1: Start with the slope formula given:
y = mx + b
Step 2: Subtract b from both sides of the equation:
y - b = mx
Step 3: Rearrange the equation by swapping sides:
mx = y - b
Step 4: Divide both sides of the equation by x to solve for m:
m = (y - b) / x
After these steps, you now have the rearranged slope formula where m is the quantity of interest.