rearange the slope formula y = mx + b for the quantity of interest m. sure to show each step.
To rearrange the slope formula y = mx + b for the quantity of interest m, we need to isolate the variable m.
Step 1: Start with the given equation: y = mx + b
Step 2: Move the constant term b to the right side of the equation by subtracting b from both sides:
y - b = mx
Step 3: Now, since mx is equivalent to m * x, to isolate m, we divide both sides by x:
(y - b) / x = m
Step 4: The final rearranged equation, solving for m, is:
m = (y - b) / x
So, the slope formula rearranged for the quantity of interest m is:
m = (y - b) / x
Dezeree received a $100 gift card and needs new sweaters for school. the sweaters cost $27.50 each. write an equation to determine how many sweaters she can buy, solve it, and determine if the value is a viable solution.
Let's write an equation to determine how many sweaters Dezeree can buy.
Let x represent the number of sweaters Dezeree can buy. Each sweater costs $27.50. The total amount that Dezeree spends on sweaters should be less than or equal to the value of her gift card ($100).
The equation can be written as:
27.50x ≤ 100
To solve for x, divide both sides of the equation by 27.50:
x ≤ 100 / 27.50
Simplifying the right side:
x ≤ 3.64
Since x represents the number of sweaters, we can conclude that Dezeree can buy a maximum of 3 sweaters with a $100 gift card.
To determine if this solution is viable, we need to check if purchasing 3 sweaters would keep Dezeree's total spending within the value of the gift card.
3 * $27.50 = $82.50
As $82.50 is less than the $100 gift card value, the solution of buying 3 sweaters is indeed viable.
To rearrange the slope formula "y = mx + b" for the quantity of interest "m," follow these steps:
Step 1: Start with the given equation: y = mx + b
Step 2: Subtract "b" from both sides of the equation to isolate "mx":
y - b = mx
Step 3: Divide both sides of the equation by "x" to solve for "m":
(y - b) / x = m
Thus, the rearranged slope formula for the quantity of interest "m" is given by: m = (y - b) / x.
To rearrange the slope formula y = mx + b for the quantity of interest m, follow these steps:
Step 1: Start with the original equation: y = mx + b
Step 2: Subtract b from both sides of the equation to isolate the "mx" term: y - b = mx
Step 3: Divide both sides of the equation by x to solve for m: (y - b) / x = m
And there you have it! The slope formula rearranged for m is: m = (y - b) / x.
By following these steps, you can easily rearrange the slope formula or any other equation to solve for a specific variable.