Question:
Use the x, y graph to derive the equation y = mx for a line through the origin. Simplify the numerical coefficient, if needed.
Answer Choices:
* y=8x
* y=x
* y=3/3x
* y=3x
To derive the equation y = mx for a line through the origin from the graph, we need to find the slope of the line. The slope (m) of a line passing through the origin and two points (x1, y1) and (x2, y2) is given by m = (y2 - y1) / (x2 - x1).
Looking at the graph, we can see that the line goes through the origin, meaning it passes through the point (0,0). Let's choose another point on the line, for example, (2,6).
So, m = (6-0)/(2-0) = 6/2 = 3
Therefore, the equation of the line passing through the origin is y = 3x.
Simplify the numerical coefficient, if needed:
y = 3x
Therefore, the correct answer choice is:
- y = 3x
The proportional relationship between inches and feet is displayed on the graph. Derive the equation of the line through the origin.
(1 point)
Responses
y=36x
y=2x
y=112x
y=12x
To derive the equation of the line representing the proportional relationship between inches and feet from the graph, we need to find the slope of the line.
The slope (m) of a line passing through the origin and two points (x1, y1) and (x2, y2) is given by m = (y2 - y1) / (x2 - x1).
Looking at the graph, start by finding two points on the line. One point is obviously (0,0) as the line passes through the origin. Another point could be (12,1) since 12 inches equals 1 foot.
m = (1 - 0) / (12 - 0) = 1 / 12
The equation of a line through the origin can be expressed as y = mx, where m is the slope.
Therefore, the equation of the line representing the proportional relationship between inches and feet is y = (1/12)x.
So, the correct answer choice is:
- y = (1/12)x
Use the table to answer the question.
x, y | (x, y)
0 | (0, )
1 | (1, )
2 | (2, )
Complete the ordered pairs in the table by finding the y - value of the ordered pairs for the equation y = 5x.
Answer Choices:
* (0, 0), (1, 5), (2, 10)
* (0, 0), (1, 1/5) , (2, 2/5)
* (0, 0), (5, 1), (10, 2)
* (0, 0), (1, 5), (3, 15)
To complete the table by finding the y-values for the equation y = 5x:
When x = 0:
y = 5 * 0 = 0
So, the ordered pair is (0, 0).
When x = 1:
y = 5 * 1 = 5
The ordered pair is (1, 5).
When x = 2:
y = 5 * 2 = 10
The ordered pair is (2, 10).
Therefore, the completed ordered pairs in the table are:
- (0, 0), (1, 5), (2, 10)
So, the correct answer choice is:
- (0, 0), (1, 5), (2, 10)
A caterer has determined that the amount of meat to order for a particular entrée varies proportionally to the number of guests. If there are 25 guests, the caterer needs to order 40 pounds of meat. How much meat should the caterer order if there are 100 guests?(1 point)
Responses
62.5 pounds
62.5 pounds
625 pounds
625 pounds
16 pounds
16 pounds
160 pounds
Since the amount of meat needed varies proportionally to the number of guests, we can set up a proportion to solve this problem.
Let x be the amount of meat the caterer should order for 100 guests.
The proportion can be set up as:
25 guests / 40 pounds = 100 guests / x pounds
Now we can cross multiply and solve for x:
25 * x = 40 * 100
25x = 4000
x = 4000 / 25
x = 160
Therefore, the caterer should order 160 pounds of meat if there are 100 guests.
The correct answer is:
160 pounds.