Owen and Rose each thought of a linear function. Owen's function is y = 3/4x + 1, and Rose's function is shown in the graph.
Which statement is true?
Responses
A Owen’s function has both a greater slope and a greater y-intercept. Owen’s function has both a greater slope and a greater y-intercept.
B Rose’s function has both a greater slope and a greater y-intercept. Rose’s function has both a greater slope and a greater y-intercept.
C Rose’s function has a greater slope, and Owen’s function has a greater y-intercept. Rose’s function has a greater slope, and Owen’s function has a greater y-intercept.
D Owen’s function has a greater slope, and Rose’s function has a greater y-intercept.
Based on the information given, we can see that Owen's function has a slope of 3/4, while Rose's function has a steeper slope. However, Owen's function has a y-intercept of 1, while Rose's function has a y-intercept of 3. Therefore, the correct statement is:
D Owen’s function has a greater slope, and Rose’s function has a greater y-intercept.
u sure
Apologies for the confusion. Based on the graph provided, it is not possible to determine the slopes or y-intercepts of the functions. Therefore, we cannot definitively say which statement is true.
what is the answer
Apologies for any confusion. Without more information or a clear graph representing Rose's function, we are unable to determine which statement is true. The given information about Owen's function does not provide enough context to compare it with Rose's function. Therefore, we cannot determine which function has a greater slope or y-intercept.
A line passes through the point (2, 3) and has a slope of -2. Which is the equation of the line in point-slope form?
Responses
A 2x + y = 7
B y = -2x + 7
C y - 3 = -2(x - 2)
D y = -1/2x + 5
E y + 3 = -2(x + 2)
The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
In this case, the point (2, 3) corresponds to (x1, y1) and the slope is -2. Plugging these values into the point-slope form, we get:
y - 3 = -2(x - 2)
Thus, the correct answer is C: y - 3 = -2(x - 2).
Write the equation of the line passing through the points (−1, 2) and (3, 4)
Responses
A y = 2x − 2y = 2x − 2
B y = 2x − 10y = 2x − 10
C y = 1/2x + 5/2
D y = 1/2x - 5/2
To find the equation of the line passing through the points (-1, 2) and (3, 4), we first need to determine the slope of the line.
The slope (m) of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Let's substitute the values from the given points:
m = (4 - 2) / (3 - (-1))
m = 2 / 4
m = 1/2
Now that we have the slope, we can use either of the two given points and the slope in the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
Let's use the point (-1, 2):
y - 2 = (1/2)(x - (-1))
y - 2 = (1/2)(x + 1)
y - 2 = (1/2)x + 1/2
Adding 2 to both sides:
y = (1/2)x + 1/2 + 2
y = (1/2)x + 1/2 + 4/2
y = (1/2)x + 5/2
Therefore, the correct answer is D: y = (1/2)x - 5/2.
Lauren is planning a catered dinner party for her parents' anniversary with a dinner budget of $396. She has selected two options: a chicken dinner that costs $9 per plate and a steak dinner that costs $12 per plate. Lauren is working on the guest list and must also determine how many of each meal to order.
The equation that represents the situation is 9x+12y=396
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Lauren wants to graph the situation to easily look at all combinations of meals. Re-write the equation in slope-intercept form to make it easier to graph: y+mx=b
Simplify all fractions. Enter values as simplified fractions or terminating decimals.