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Oxana [17]
3 years ago
15

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

Mathematics
1 answer:
Dimas [21]3 years ago
3 0

Answer:

4) The linear equation which could represent its image is y = \frac{3}{4} x + 8 ⇒ (2)

5) The equation of the image of the line is y = \frac{3}{2} 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 = \frac{3}{4} x + 2 ⇒ the equation of the line before dilation

- By comparing it with the form above, then m =  \frac{3}{4} , so the

   equation after dilation has the same slope

∵ The slope of the line before dilation is  \frac{3}{4}

∴ The slope of the line after dilation is  \frac{3}{4}

∵ The equation that has the slope  \frac{3}{4}  is y =

∴ The equation of the image of the line is y = \frac{3}{4} x + 8

The linear equation which could represent its image is y = \frac{3}{4} x + 8

5)

∵ The equation of the line is y = \frac{3}{2} x - 4

∵ The scale factor of dilation is \frac{3}{4}

- Dilation dose not change the slope of the line

∴ The slope of the image after dilation is \frac{3}{2}

- 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 \frac{3}{4}

∵  \frac{3}{4} × -4 = -3

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

∴ The equation of the image of the line is y = \frac{3}{2} x - 3

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