Final Answer:
y = 1.5X is the linear equation that represents the relationship between the amount of grams in fish X and the number of calories y. For every gram of fish, there are 1.5 calories.
Step-by-step explanation:
To write an equation of a line that goes through the points (100, 150) and (200, 300), we will use the slope-intercept form of a line, which is:
y = mx + b
Where:
y is the dependent variable (number of calories),
mis the slope of the line,
x is the independent variable (amount of grams in fish), and
b is the y-intercept.
First, let's determine the slope m using the formula:
m = (y₂-y₁) / (x₂-x₁)
Plugging in our points:
x₁ = 100, y₁ = 150,
x₂ = 200, y₂ = 300.
The slope is:
m = (300 - 150)/(200 - 100)
m = (150)/(100)
m = 3/2
m = 1.5
Now that we have the slope, we need to find the y-intercept b. We can use either of the given points and the slope to find b using this rearranged form of our line equation:
b = y - mx
Using the first point (100, 150), we have:
b = 150 - (1.5 × 100)
b = 150 - 150
b = 0
So our y-intercept b is 0.
Now we can write the final equation of the line using the values of m and b:
y = 1.5x + 0
Or simplified further:
y = 1.5X
So, the asked linear equation is y = 1.5X.
Complete question:
Write an equation that reflects this relationship using X to represent the amount of grams in fish and y to represent the number of calories. Here the line passing through points (100, 150) and (200, 300)