Question
Some eighth graders are making muffins for a fund raiser. They have already made 200 muffins and figure they can make 40 muffins in an hour.
a) Write a linear function in the form Y= mx + b that represents the total no. of muffins the students will make, y, and the number of additional hours spent making the muffins ,x.
b) How many additional hours would the students spend to make 640 muffins?
Hint:
Already made 200 muffins will act as y – intercept
The correct answer is: a) y = 40x + 200, b) 11 hours
SOL – No of additional hours spent making the muffins = x
Total no. of muffins = y
(a) It is given that rate of making muffins is 40 muffins per hour
i.e. Slope of the graph = 40
It is given that they have already made 200 muffins i.e. when x = 0 , y = 200
So, y – intercept, c = 200
Using slope – intercept form, equation of the line is
y = mx + c
y = 40x + 200
(b) Acc. to question, y = 640
640 = 40x + 200
440 = 40x
11 = x
So, it took additional 11 hours to make 640 muffins.
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The graph shows the relationship between the number of cubic yards of mulch ordered and the total cost of the mulch delivered. What is the constant rate of change? What does it represent ? What is the initial value ? What might that represent?
The form of a linear equation is y = mx + b in the slope-intercept notation. Variables in the equation are the X and Y. The values m and b represent the line's slope (m) and the value of y when x is 0 and Y is 500. (b). Because the line crosses the y-axis at (0,y), when x is 0, y is referred to as the y-intercept. A two-variable linear equation can be thought of as a linear relationship between y and x or two variables where the value of one (often y) relies on the value of the other (usually x). In this scenario, x is referred to be an independent variable and y as a dependent variable because it depends on the x variable.
Often plotted along the horizontal axis represents the independent variable, x label or not. The majority of linear equations are functions. Alternatively, there is just one value of y for every value of x. You can calculate the value of the dependent variable, y, once the independent variable, x, has been given a value.
The graph shows the relationship between the number of cubic yards of mulch ordered and the total cost of the mulch delivered. What is the constant rate of change? What does it represent ? What is the initial value ? What might that represent?
The form of a linear equation is y = mx + b in the slope-intercept notation. Variables in the equation are the X and Y. The values m and b represent the line's slope (m) and the value of y when x is 0 and Y is 500. (b). Because the line crosses the y-axis at (0,y), when x is 0, y is referred to as the y-intercept. A two-variable linear equation can be thought of as a linear relationship between y and x or two variables where the value of one (often y) relies on the value of the other (usually x). In this scenario, x is referred to be an independent variable and y as a dependent variable because it depends on the x variable.
Often plotted along the horizontal axis represents the independent variable, x label or not. The majority of linear equations are functions. Alternatively, there is just one value of y for every value of x. You can calculate the value of the dependent variable, y, once the independent variable, x, has been given a value.
