4) The line -3x + 4y = 8 is transformed by a dilation centered at the origin. Which linear equation could represent its image?
(1) y = 43x + 8 (3) y = -34x - 8

(2) y = 34x + 8 (4) y = -43x – 8

5) What is an equation of the image of the line y = 32x - 4 after a dilation of a scale factor of 34 centered at the origin?
(1) y = 98x - 4 (3) y = 32x - 4
(2) y = 98x - 3 (4) y = 32x – 3

4) The linear equation which could represent its image is y = x + 8 ⇒ (2)

5) The equation of the image of the line is y = x - 3 ⇒ (4)

Step-by-step explanation:

Dilation does not change the slope of a line but changes the y-intercept

Dilation of a line segment is longer or shorter by ratio that equal to the scale factor of dilation

4)

The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b its y-intercept

Let us put the given equation in the slope-intercept form to find its slope

∵ The line -3x + 4y = 8 is transformed by a dilation centered at

   the origin

- Add 3x to both sides

∴ 4y = 3x + 8

- Divide both sides by 4

∴ y = x + 2 ⇒ the equation of the line before dilation

- By comparing it with the form above, then m =   , so the

   equation after dilation has the same slope

∵ The slope of the line before dilation is  

∴ The slope of the line after dilation is  

∵ The equation that has the slope    is y =

∴ The equation of the image of the line is y = x + 8

The linear equation which could represent its image is y = x + 8

5)

∵ The equation of the line is y = x - 4

∵ The scale factor of dilation is

- Dilation dose not change the slope of the line

∴ The slope of the image after dilation is

- Dilation changes the y-intercept, to find it multiply the scale

  factor of dilation by the y-intercept of the line before dilation

∵ The y-intercept of the line is (0 , -4)

- Multiply it by

∵   × -4 = -3

∴ The y-intercept of the image is (0 , -3)

∴ The equation of the image of the line is y = x - 3

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.