Use similar triangles to determine the slope of the line. (1 point)
Given the points (3,9), (2,6), (1,3), (0,0), we can determine the slope of the line using similar triangles.
Let's consider the points (2,6) and (1,3).
The vertical change between these two points is: Δy = 6 - 3 = 3
The horizontal change between these two points is: Δx = 2 - 1 = 1
Therefore, the slope of the line is: m = Δy/Δx = 3/1 = 3
To determine the slope of a line using similar triangles, we need to compare the vertical and horizontal changes between two points on the line.
Let's consider two points on the line: (x₁, y₁) and (x₂, y₂)
The vertical change between these two points is: Δy = y₂ - y₁
The horizontal change between these two points is: Δx = x₂ - x₁
The slope of the line is defined as the ratio of vertical change to horizontal change: m = Δy/Δx
So, to determine the slope of the line using similar triangles, we can compare the vertical and horizontal changes between two points.
so whats the answer?
Without specific information about the specific points and their coordinates on the line, it is not possible to determine the slope using similar triangles. The slope can only be determined if we have the coordinates of two points on the line.
The graph shows (3,9) (2,6) (1,3) (0,0)
How could you write the equation of a line that would be parallel to y=−3x−2 but not share any points?(1 point) Responses y=3x−2 y equals 3 x minus 2 y=3x+8 y equals 3 x plus 8 y=−3x+8 y equals negative 3 x plus 8 y=−3x−2
To write the equation of a line that would be parallel to y = -3x - 2 but not share any points, we need to keep the same slope (-3) and choose a different y-intercept.
The equation of the parallel line could be written as: y = -3x + b, where b is any real number different from -2.
Therefore, the correct response from the given options is: y = -3x + 8
Use the table to answer the question. ($) Cost of Candy Bar 1 Quantity ($) Cost 1 1.25 2 2.50 3 3.75 4 5.00 5 6.25 The cost of Candy Bar 1 is displayed in the table. The proportional relationship between the cost and quantity for Candy Bar 2 is represented by the equation y=x . Which candy bar is the cheapest cost per bar? Enter 1 for Candy Bar 1. Enter 2 for Candy Bar 2. (1 point)
To determine which candy bar has the cheapest cost per bar, we need to calculate the cost per bar for each candy bar.
For Candy Bar 1:
Quantity: 1
Cost: $1.25
Cost per bar = Cost/Quantity = $1.25/1 = $1.25
For Candy Bar 2:
Quantity: 2
Cost: y = x, where x is the quantity
Cost per bar = Cost/Quantity = (y/2)/2 = y/4
Since the equation representing the proportional relationship between the cost and quantity for Candy Bar 2 is y = x, the cost per bar for Candy Bar 2 is also x/4.
Comparing the two cost per bar expressions, we can see that the cost per bar for Candy Bar 1 is a constant $1.25, while the cost per bar for Candy Bar 2 depends on the quantity.
Therefore, Candy Bar 1 has the cheapest cost per bar. Enter 1 for Candy Bar 1.
Use the graph to derive the equation of the line in slope-intercept form.
The graph shows (1,3) and (0,-2)
To derive the equation of the line in slope-intercept form, we need to calculate the slope and the y-intercept using the given points (1, 3) and (0, -2).
First, let's find the slope (m):
m = (y₂ - y₁)/(x₂ - x₁)
m = (-2 - 3)/(0 - 1)
m = (-5)/(-1)
m = 5
Now, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept. We can substitute the slope (m) and one of the given points (x, y) into the equation to find b.
Using the point (1, 3):
3 = 5(1) + b
3 = 5 + b
b = 3 - 5
b = -2
Therefore, the equation of the line in slope-intercept form is:
y = 5x - 2
Describe what makes a proportion. Give an example of a proportion.(2 points)
make it original please!
A proportion is a mathematical statement that expresses the equality of two ratios. It shows the relationship between two sets of numbers or quantities, indicating that they are equivalent.
For example, consider the following proportion:
4/8 = 2/4
In this proportion, the ratio of 4 to 8 is equivalent to the ratio of 2 to 4. It says that for every 4 units in the first set, there are 8 units in the second set, and for every 2 units in the first set, there are 4 units in the second set. The two ratios are equal, implying that the proportion holds true.