the museum charges $20 dollars for two people. and 28 for three people
what is the equation that realtes the number of people in a group and the cost to enter a museum? write it in slope intercept form
To find the equation that relates the number of people in a group and the cost to enter a museum, we can first observe the given information:
For two people, the cost is $20.
For three people, the cost is $28.
Let's define the number of people as x and the cost as y.
We can interpret this information as two points on the graph: (2, 20) and (3, 28). Now, let's find the slope-intercept form of the equation.
The slope-intercept form of an equation is y = mx + b, where m represents the slope and b represents the y-intercept.
Step 1: Find the slope (m):
The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).
Using the given points (2, 20) and (3, 28):
m = (28 - 20) / (3 - 2)
m = 8 / 1
m = 8
Step 2: Find the y-intercept (b):
We can substitute one of the points into the equation (2, 20) to find the value of b.
Using the point (2, 20) and the slope (m = 8):
20 = 8(2) + b
20 = 16 + b
b = 20 - 16
b = 4
Step 3: Write the equation:
Now that we have the slope (m = 8) and the y-intercept (b = 4), the equation that relates the number of people (x) and the cost (y) is:
y = 8x + 4
Therefore, the equation in slope-intercept form is y = 8x + 4.