Question

A model of a building is 27.5 inches tall. The scale of the model is 1 inch : 9 feet.
What is the height of the building?

Answer 1

To find the height of the building, we need to use the scale factor of 1 inch : 9 feet.
Since the model is 27.5 inches tall, we can set up a proportion to find the actual height of the building.

1 inch = 9 feet
27.5 inches = x feet

1/9 = 27.5/x

Cross multiplying, we get:
1x = 27.5*9
x = 247.5

Therefore, the height of the building is 247.5 feet tall.

Answer 2

Use the image to answer the question.

An illustration of a scatterplot graph shows x-axis ranging from 0 to 10 in increments of 1 and y-axis ranging from 0 to 50 in increments of 10. Multiple points are plotted around a line that points downward to the right with an arrowhead on the bottom.
The line passes approximately through left parenthesis 0 comma 45 right parenthesis, left parenthesis 2 comma 25 right parenthesis, left parenthesis 3 comma 15 right parenthesis, and left parenthesis 4.5 comma 0 right parenthesis. 13 points are plotted close to the line.

Write an equation in slope-intercept form of the trend line.

Answer 3

To find the equation of the trend line in slope-intercept form, we need to determine the slope and y-intercept based on the given points.

Using the points given: (0, 45), (2, 25), (3, 15), and (4.5, 0), we can calculate the slope:
Slope (m) = (y2 - y1) / (x2 - x1)

For point (0, 45) and (4.5, 0):
m = (0 - 45) / (4.5 - 0) = -45 / 4.5 = -10

Now that we have the slope, we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)

Using point (0, 45):
y - 45 = -10(x - 0)
y - 45 = -10x
y = -10x + 45

Therefore, the equation of the trend line in slope-intercept form is y = -10x + 45.

Answer 4

Use the image to answer the question.

An illustration of a scatterplot graph shows x-axis ranging from 0 to 10 in increments of 1 and y-axis ranging from 0 to 30 in increments of 2. Multiple points are plotted around a line that points upward to the right with an arrowhead on the bottom.
The line passes approximately through left parenthesis 0 comma 12 right parenthesis, left parenthesis 4 comma 16 right parenthesis, and left parenthesis 6 comma 18 right parenthesis. 12 points are plotted close to the line.

Write an equation in slope-intercept form of the trend line.

Answer 5

To find the equation of the trend line in slope-intercept form, we need to determine the slope and y-intercept based on the given points.

Using the points given: (0, 12), (4, 16), and (6, 18), we can calculate the slope:
Slope (m) = (y2 - y1) / (x2 - x1)

For the points given:
m = (16 - 12) / (4 - 0) = 4 / 4 = 1

Now that we have the slope, we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)

Using point (0, 12):
y - 12 = 1(x - 0)
y - 12 = x
y = x + 12

Therefore, the equation of the trend line in slope-intercept form is y = x + 12.